### Course

19S1 D. Anselmi
Theories of gravitation

Program

PDF

### Book

D. Anselmi
From Physics To Life

A journey to the infinitesimally small and back

In English and Italian

Available on Amazon:
US: book | ebook  (in EN)
IT: book | ebook  (in IT)

## 22A2 Damiano AnselmiFakeons versus Lee-Wick ghosts: physical Pauli-Villars fields, finite QED and quantum gravity

We reconsider the Lee-Wick (LW) models and compare their properties to the properties of the models that contain purely virtual particles. We argue against the LW premise that unstable particles can be removed from the sets of incoming and outgoing states in scattering processes. The removal leads to a non-Hermitian... read more

## 22A1 Damiano AnselmiDressed propagators, fakeon self-energy and peak uncertainty

We study the resummation of self-energy diagrams into dressed propagators in the case of purely virtual particles and compare the results with those obtained for physical particles and ghosts. The three geometric series differ by infinitely many contact terms, which do not admit well-defined sums. The peak region, which is... read more

## 21A5 Damiano AnselmiDiagrammar of physical and fake particles and spectral optical theorem

We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman $i\epsilon$ prescription) and purely virtual particles (defined by the fakeon prescription). The identities are derived by means of purely algebraic operations and hold for every (multi)threshold separately and for arbitrary frequencies. Their major... read more

## 21A4 Damiano Anselmi, Kristjan Kannike, Carlo Marzo, Luca Marzola, Aurora Melis, Kristjan Müürsepp, Marco Piva and Martti RaidalA fake doublet solution to the muon anomalous magnetic moment

Extensions to the Standard Model that use strictly off-shell degrees of freedom – the fakeons – allow for new measurable interactions at energy scales usually precluded by the constraints that target the on-shell propagation of new particles. Here we employ the interactions between a new fake scalar doublet and the... read more

## 21A3 Damiano Anselmi, Kristjan Kannike, Carlo Marzo, Luca Marzola, Aurora Melis, Kristjan Müürsepp, Marco Piva, Martti RaidalPhenomenology of a Fake Inert Doublet Model

We introduce a new way of modeling the physics beyond the Standard Model by considering fake, strictly off-shell degrees of freedom: the fakeons. To demonstrate the approach and exemplify its reach, we re-analyze the phenomenology of the Inert Doublet Model under the assumption that the second doublet is a fakeon.... read more

## 21A2 Damiano AnselmiPerturbation spectra and renormalization-group techniques in double-field inflation and quantum gravity cosmology

We study primordial cosmology with two scalar fields that participate in inflation at the same time, by coupling quantum gravity (i.e., the theory $R+R^2+C^2$ with the fakeon prescription/projection for $C^2$) to a scalar field with a quadratic potential. We show that there exists a perturbative regime that can be described by... read more

## 21A1 Damiano Anselmi, Filippo Fruzza and Marco PivaRenormalization-group techniques for single-field inflation in primordial cosmology and quantum gravity

We study inflation as a “cosmic” renormalization-group flow. The flow, which encodes the dependence on the background metric, is described by a running coupling $\alpha$, which parametrizes the slow roll, a de Sitter free, analytic beta function and perturbation spectra that are RG invariant in the superhorizon limit. Using... read more

## 20A5 Damiano AnselmiHigh-order corrections to inflationary perturbation spectra in quantum gravity

We compute the inflationary perturbation spectra and the quantity $r+8n_{T}$ to the next-to-next-to-leading log order in quantum gravity with purely virtual particles (which means the theory $R+R^{2}+C^{2}$ with the fakeon prescription/projection for $C^{2}$). The spectra are functions of the inflationary running coupling $\alpha (1/k)$ and satisfy the cosmic renormalization-group flow... read more

## 20A4 Damiano AnselmiCosmic inflation as a renormalization-group flow: the running of power spectra in quantum gravity

We study the running of power spectra in inflationary cosmology as a renormalization-group flow from the de Sitter fixed point. The beta function is provided by the equations of the background metric. The spectra of the scalar and tensor fluctuations obey RG evolution equations with vanishing anomalous dimensions in the... read more

## 20A3 Damiano AnselmiQuantum field theories of arbitrary-spin massive multiplets and Palatini quantum gravity

We formulate quantum field theories of massive fields of arbitrary spins. The presence of both physical and fake particles, organized into multiplets, makes it possible to fulfill the requirements of locality, unitarity and renormalizability at the same time. The theories admit cubic and quartic self-interactions and can be coupled to... read more

## 20A2 Damiano Anselmi, Eugenio Bianchi and Marco PivaPredictions of quantum gravity in inflationary cosmology: effects of the Weyl-squared term

We derive the predictions of quantum gravity with fakeons on the amplitudes and spectral indices of the scalar and tensor fluctuations in inflationary cosmology. The action is $R+R^{2}$ plus the Weyl-squared term. The ghost is eliminated by turning it into a fakeon, that is to say a purely virtual particle.... read more

## 20A1 Damiano AnselmiThe quest for purely virtual quanta: fakeons versus Feynman-Wheeler particles

The search for purely virtual quanta has attracted interest in the past. We consider various proposals and compare them to the concept of fake particle, or “fakeon”. In particular, the Feynman-Wheeler propagator, which amounts to using the Cauchy principal value inside Feynman diagrams, violates renormalizability, unitarity and stability, due to... read more

## 19A3 Damiano Anselmi and Antonio MarinoFakeons and microcausality: light cones, gravitational waves and the Hubble constant

The concept of fake particle, or “fakeon”, allows us to make sense of quantum gravity as an ultraviolet complete theory, by renouncing causality at very small distances. We investigate whether the violation of microcausality can be amplified or detected in the most common settings. We show that it is actually... read more

## 19A2 Damiano AnselmiFakeons, unitarity, massive gravitons and the cosmological constant

We give a simple proof of perturbative unitarity in gauge theories and quantum gravity using a special gauge that allows us to separate the physical poles of the free propagators, which are quantized by means of the Feynman prescription, from the poles that belong to the gauge-trivial sector, which are... read more

## 19A1 Damiano AnselmiFakeons and the classicization of quantum gravity: the FLRW metric

Under certain assumptions, it is possible to make sense of higher derivative theories by quantizing the unwanted degrees of freedom as fakeons, which are later projected away. Then the true classical limit is obtained by classicizing the quantum theory. Since quantum field theory is formulated perturbatively, the classicization is also... read more

## 18A7 Damiano AnselmiOn the nature of the Higgs boson

Several particles are not observed directly, but only through their decay products. We consider the possibility that they might be fakeons, i.e. fake particles, which mediate interactions but are not asymptotic states. A crucial role to determine the true nature of a particle is played by the imaginary parts of... read more

## 18A6 Damiano AnselmiLet the dice play God

We define life as the amplification of quantum uncertainty up to macroscopic scales. A living being is any amplifier that achieves this goal. We argue that everything we know about life can be explained from this idea. We study a ladder mechanism to estimate... read more

## 18A5 Damiano AnselmiThe correspondence principle in quantum field theory and quantum gravity

We discuss the fate of the correspondence principle beyond quantum mechanics, specifically in quantum field theory and quantum gravity, in connection with the intrinsic limitations of the human ability to observe the external world. We conclude that the best correspondence principle is made of unitarity, locality, proper renormalizability (a refinement... read more

## 18A4 Damiano AnselmiFakeons, microcausality and the classical limit of quantum gravity

We elaborate on the idea of fake particle and study its physical consequences. When a theory contains fakeons, the true classical limit is determined by the quantization and a subsequent process of “classicization”. One of the major predictions due to the fake particles is the violation of microcausality, which survives... read more

## 18A1 Damiano AnselmiFakeons and Lee-Wick models

The “fakeon” is a fake degree of freedom, i.e. a degree of freedom that does not belong to the physical spectrum, but propagates inside the Feynman diagrams. Fakeons can be used to make higher-derivative theories unitary. Moreover, they help us clarify how the Lee-Wick models work. In this paper we... read more

## 17A3 Damiano AnselmiOn the quantum field theory of the gravitational interactions

We study the main options for a unitary and renormalizable, local quantum field theory of the gravitational interactions. The first model is a Lee-Wick superrenormalizable higher-derivative gravity, formulated as a nonanalytically Wick rotated Euclidean theory. We show that, under certain conditions, the $S$ matrix is unitary when the cosmological constant... read more

## 17A2 Damiano Anselmi and Marco PivaPerturbative unitarity of Lee-Wick quantum field theory

We study the perturbative unitarity of the Lee-Wick models, formulated as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions and the values of a loop integral in the various regions are related to one another by a nonanalytic procedure. We show that the one-loop... read more

## 17A1 Damiano Anselmi and Marco PivaA new formulation of Lee-Wick quantum field theory

The Lee-Wick models are higher-derivative theories that are claimed to be unitary thanks to a peculiar cancelation mechanism. In this paper, we provide a new formulation of the models, to clarify several aspects that have remained quite mysterious, so far. Specifically, we define them as nonanalytically Wick rotated Euclidean theories.... read more

## 16A3 Damiano AnselmiAlgebraic cutting equations

The cutting equations are diagrammatic identities that are used to prove perturbative unitarity in quantum field theory. In this paper, we derive algebraic, upgraded versions of them. Differently from the diagrammatic versions, the algebraic identities also holds for propagators with arbitrary, nonvanishing widths. In particular, the cut propagators do not... read more

## 16A2 Ugo G. Aglietti and Damiano AnselmiInconsistency of Minkowski higher-derivative theories

We show that Minkowski higher-derivative quantum field theories are generically inconsistent, because they generate nonlocal, non-Hermitian ultraviolet divergences, which cannot be removed by means of standard renormalization procedures. By “Minkowski theories” we mean theories that are defined directly in Minkowski spacetime. The problems occur when the propagators have complex poles,... read more

## 16A1 Damiano AnselmiAspects of perturbative unitarity

We reconsider perturbative unitarity in quantum field theory and upgrade several arguments and results. The minimum assumptions that lead to the largest time equation, the cutting equations and the unitarity equation are identified. Using this knowledge and a special gauge, we give a new, simpler proof of perturbative unitarity in... read more

## 15A4 Damiano AnselmiBackground field method and the cohomology of renormalization

Using the background field method and the Batalin-Vilkovisky formalism, we prove a key theorem on the cohomology of perturbatively local functionals of arbitrary ghost numbers, in renormalizable and nonrenormalizable quantum field theories whose gauge symmetries are general covariance, local Lorentz symmetry, non-Abelian Yang-Mills symmetries and Abelian gauge symmetries. Interpolating between... read more

## 15A3 Damiano AnselmiSome reference formulas for the generating functions of canonical transformations

We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then, we propose a standard way... read more

## 15A2 Damiano AnselmiAdler-Bardeen theorem and cancellation of gauge anomalies to all orders in nonrenormalizable theories

We prove the Adler-Bardeen theorem in a large class of general gauge theories, including nonrenormalizable ones. We assume that the gauge symmetries are general covariance, local Lorentz symmetry and Abelian and non-Abelian Yang-Mills symmetries, and that the local functionals of vanishing ghost numbers satisfy a variant of the Kluberg-Stern–Zuber conjecture.... read more

## 15A1 Damiano AnselmiWard identities and gauge independence in general chiral gauge theories

Using the Batalin-Vilkovisky formalism, we study the Ward identities and the equations of gauge dependence in potentially anomalous general gauge theories, renormalizable or not. A crucial new term, absent in manifestly nonanomalous theories, is responsible for interesting effects. We prove that gauge invariance always implies gauge independence, which in turn... read more

## 14A2 D. Anselmi Weighted power counting and chiral dimensional regularization

We define a modified dimensional-regularization technique that overcomes several difficulties of the ordinary technique, and is specially designed to work efficiently in chiral and parity violating quantum field theories, in arbitrary dimensions greater than 2. When the dimension of spacetime is continued to complex values, spinors, vectors and tensors keep... read more

## 14A1 D. Anselmi Adler-Bardeen theorem and manifest anomaly cancellation to all orders in gauge theories

We reconsider the Adler-Bardeen theorem for the cancellation of gauge anomalies to all orders, when they vanish at one loop. Using the Batalin-Vilkovisky formalism and combining the dimensional-regularization technique with the higher-derivative gauge invariant regularization, we prove the theorem in the most general perturbatively unitary renormalizable gauge theories coupled to... read more

## 13A3 D. Anselmi Background field method, Batalin-Vilkovisky formalism and parametric completeness of renormalization

We investigate the background field method with the Batalin-Vilkovisky formalism, to generalize known results, study parametric completeness and achieve a better understanding of several properties. In particular, we study renormalization and gauge dependence to all orders. Switching between the background field approach and the usual approach by means of canonical... read more

## 13A2 D. Anselmi Properties of the classical action of quantum gravity

The classical action of quantum gravity, determined by renormalization, contains infinitely many independent couplings and can be expressed in different perturbatively equivalent ways. We organize it in a convenient form, which is based on invariants constructed with the Weyl tensor. We show that the FLRW metrics are exact solutions of the field equations in arbitrary... read more

## 13A1 D. Anselmi Renormalization of gauge theories without cohomology

We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional... read more

## 12A3 D. Anselmi Master functional and proper formalism for quantum gauge field theory

We develop a general field-covariant approach to quantum gauge theories. Extending the usual set of integrated fields and external sources to “proper” fields and sources, which include partners of the composite fields, we define the master functional $\Omega$, which collects one-particle irreducible diagrams and upgrades the usual $\Gamma$-functional in several... read more

## 12A2 D. Anselmi A master functional for quantum field theory

We study a new generating functional of one-particle irreducible diagrams in quantum field theory, called master functional, which is invariant under the most general perturbative changes of field variables. The functional $\Gamma$ does not transform as a scalar under the transformation law inherited from its very definition, although it does... read more

## 12A1 D. Anselmi A general field-covariant formulation of quantum field theory

In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and parameters. Because of this, we cannot write simple identities relating bare and renormalized generating functionals,... read more

## 11A2 Damiano Anselmi and Martina Taiuti Vacuum Cherenkov radiation in quantum electrody-namics with high-energy Lorentz violation

We study phenomena predicted by a renormalizable, CPT invariant extension of the Standard Model that contains higher-dimensional operators and violates Lorentz symmetry explicitly at energies greater than some scale $\Lambda_{L}$. In particular, we consider the Cherenkov radiation in vacuo. In a rather general class of dispersion relations, there exists an... read more

## 11A1 Damiano Anselmi and Emilio CiuffoliLow-energy phenomenology of scalarless standard model extensions with high-energy Lorentz violation

We consider renormalizable Standard-Model extensions that violate Lorentz symmetry at high energies, but preserve CPT, and do not contain elementary scalar fields. A Nambu–Jona-Lasinio mechanism gives masses to fermions and gauge bosons, and generates composite Higgs fields at low energies. We study the effective potential at the leading order of... read more

## 10A1 D. Anselmi and E. Ciuffoli Renormalization of high-energy Lorentz violating four fermion models

We study the one-loop renormalization of high-energy Lorentz violating four fermion models. We derive general formulas and then consider a number of specific models. We study the conditions for asymptotic freedom and give a practical method to determine the asymptotic-freedom domain. We also point out that in some models the... read more

## 09A2 Damiano Anselmi and Martina Taiuti Renormalization of high-energy Lorentz violating QED

We study a QED extension that is unitary, CPT invariant and super-renormalizable, but violates Lorentz symmetry at high energies, and contains higher-dimension operators (LVQED). Divergent diagrams are only one- and two-loop. We compute the one-loop renormalizations at high and low energies and analyse the relation between them. It emerges that... read more

## 09A1 Damiano Anselmi Standard Model without elementary scalars and high energy Lorentz violation

If Lorentz symmetry is violated at high energies, interactions that are usually non-renormalizable can become renormalizable by weighted power counting. Recently, a CPT invariant, Lorentz violating extension of the Standard Model containing two scalar-two fermion interactions (which can explain neutrino masses) and four fermion interactions (which can explain proton decay) was proposed.... read more

## 08A4 Damiano Anselmi Weighted power counting, neutrino masses and Lorentz violating extensions of the Standard Model

We study the Standard-Model extensions that have the following features: they violate Lorentz invariance explicitly at high energies; they are unitary, local, polynomial and renormalizable by weighted power counting; they contain the vertex $(LH)^2$, which gives Majorana masses to the neutrinos after symmetry breaking, and possibly four fermion interactions; they... read more

## 08A3 D. Anselmi Weighted power counting and Lorentz violating gauge theories. II: Classification

We classify the local, polynomial, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. We study the structure of such theories and prove that renormalization does not generate higher time derivatives. We work out the conditions to renormalize vertices that are... read more

## 08A2 D. Anselmi Weighted power counting and Lorentz violating gauge theories. I: General properties

We construct local, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. They contain higher space derivatives, which improve the behavior of propagators at large momenta, but no higher time derivatives. We show that the regularity of the gauge-field propagator privileges... read more

## 08A1 D. Anselmi Weighted scale invariant quantum field theories

We study a class of Lorentz violating quantum field theories that contain higher space derivatives, but no higher time derivatives, and become renormalizable in the large N expansion. The fixed points of their renormalization-group flows provide examples of exactly “weighted scale invariant” theories, which are noticeable Lorentz violating generalizations of conformal field theories. We classify... read more

## 07A2 Damiano Anselmi and Milenko Halat Renormalization of Lorentz violating theories

We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not generated by renormalization. Renormalizability is ensured by a “weighted power counting” criterion. The theories contain a dimensionful... read more

## 07A1 Damiano Anselmi and Anna Benini Improved Schwinger-DeWitt techniques for higher-derivative perturbations of operator determinants

We consider higher-derivative perturbations of quantum gravity and quantum field theories in curved space and investigate tools to calculate counterterms and short-distance expansions of Feynman diagrams. In the case of single higher-derivative insertions we derive a closed formula that relates the perturbed one-loop counterterms to the unperturbed Schwinger-DeWitt coefficients. In... read more

## 06A2 Damiano Anselmi and Milenko Halat Renormalizable acausal theories of classical gravity coupled with interacting quantum fields

We prove the renormalizability of various theories of classical gravity coupled with interacting quantum fields. The models contain vertices with dimensionality greater than four, a finite number of matter operators and a finite or reduced number of independent couplings. An interesting class of models is obtained from ordinary power-counting renormalizable... read more

## 06A1 D. Anselmi Renormalization and causality violations in classical gravity coupled with quantum matter

I prove that classical gravity coupled with quantized matter can be renormalized with a finite number of independent couplings, plus field redefinitions, without introducing higher-derivative kinetic terms in the gravitational sector, but adding vertices that couple the matter stress-tensor with the Ricci tensor. The theory is called “acausal gravity”, because... read more

## 05A3 Damiano Anselmi and Milenko Halat Dimensionally continued infinite reduction of couplings

The infinite reduction of couplings is a tool to consistently renormalize a wide class of non-renormalizable theories with a reduced, eventually finite, set of independent couplings, and classify the non-renormalizable interactions. Several properties of the reduction of couplings, both in renormalizable and non-renormalizable theories, can be better appreciated working at... read more

## 05A2 D. Anselmi Infinite reduction of couplings in non-renormalizable quantum field theory

I study the problem of renormalizing a non-renormalizable theory with a reduced, eventually finite, set of independent couplings. The idea is to look for special relations that express the coefficients of the irrelevant terms as unique functions of a reduced set of independent couplings $\lambda$, such that the divergences are... read more

## 05A1 D. Anselmi Renormalization of a class of non-renormalizable theories

Certain power-counting non-renormalizable theories, including the most general self-interacting scalar fields in four and three dimensions and fermions in two dimensions, have a simplified renormalization structure. For example, in four-dimensional scalar theories, $2n$ derivatives of the fields, $n>1$, do not appear before the nth loop. A new kind of expansion... read more

## 04A2 D. Anselmi Deformed dimensional regularization for odd (and even) dimensional theories

I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with the trace of an odd product of gamma matrices in odd dimensions. The regularization is completed with an... read more

## 04A1 Damiano Anselmi A note on the dimensional regularization of the Stan-dard Model coupled with quantum gravity

In flat space, $\gamma_5$ and the epsilon tensor break the dimensionally continued Lorentz symmetry, but propagators have fully Lorentz invariant denominators. When the Standard Model is coupled with quantum gravity $\gamma_5$ breaks the continued local Lorentz symmetry. I show how to deform the Einstein lagrangian and gauge-fix the residual local... read more

## 03A3 D. Anselmi Consistent irrelevant deformations of interacting conformal field theories

I show that under certain conditions it is possible to define consistent irrelevant deformations of interacting conformal field theories. The deformations are finite or have a unique running scale (“quasi-finite”). They are made of an infinite number of lagrangian terms and a finite number of independent parameters that renormalize coherently.... read more

## 03A2 D. Anselmi Finiteness of quantum gravity coupled with matter in three spacetime dimensions

As it stands, quantum gravity coupled with matter in three spacetime dimensions is not finite. In this paper I show that an algorithmic procedure that makes it finite exists, under certain conditions. To achieve this result, gravity is coupled with an interacting conformal field theory $C$. The Newton constant and... read more

## 03A1 D. Anselmi Renormalization of quantum gravity coupled with matter in three dimensions

In three spacetime dimensions, where no graviton propagates, pure gravity is known to be finite. It is natural to inquire whether finiteness survives the coupling with matter. Standard arguments ensure that there exists a subtraction scheme where no Lorentz-Chern-Simons term is generated by radiative corrections, but are not sufficiently powerful... read more

## 02A4 D. Anselmi Absence of higher derivatives in the renormalization of propagators in quantum field theories with infinitely many couplings

I study some aspects of the renormalization of quantum field theories with infinitely many couplings in arbitrary space-time dimensions. I prove that when the space-time manifold admits a metric of constant curvature the propagator is not affected by terms with higher derivatives. More generally, certain lagrangian terms are not turned... read more

## 02A3 D. Anselmi Inequalities for trace anomalies, length of the RG flow, distance between the fixed points and irreversibility

I discuss several issues about the irreversibility of the RG flow and the trace anomalies $c$, $a$ and $a’$. First I argue that in quantum field theory: $i$) the scheme-invariant area $\Delta a’$ of the graph of the effective beta function between the fixed points defines the length of the... read more

## 02A2 D. Anselmi “Integrability” of RG flows and duality in three dimensions in the 1/N expansion

I study some classes of RG flows in three dimensions that are classically conformal and have manifest $g \rightarrow 1/g$ dualities. The RG flow interpolates between known (four-fermion, Wilson-Fischer, $\phi_3^6$) and new interacting fixed points. These models have two remarkable properties: $i$) the RG flow can be integrated for arbitrarily... read more

## 02A1 D. Anselmi Sum rules for trace anomalies and irreversibility of the renormalization-group flow

I review my explanation of the irreversibility of the renormalization-group flow in even dimensions greater than two and address new investigations and tests.

PDF

Acta Phys.Slov. 52 (2002) 573

arXiv:hep-th/0205039

## 01A3 D. Anselmi A note on the improvement ambiguity of the stress tensor and the critical limits of correlation functions

I study various properties of the critical limits of correlators containing insertions of conserved and anomalous currents. In particular, I show that the improvement term of the stress tensor can be fixed unambiguously, studying the RG interpolation between the UV and IR limits. The removal of the improvement ambiguity is... read more

## 01A2 D. Anselmi Kinematic sum rules for trace anomalies

I derive a procedure to generate sum rules for the trace anomalies $a$ and $a’$. Linear combinations of $\Delta a = a_{UV}-a_{IR}$ and $\Delta a’ = a’_{UV}-a’_{IR}$ are expressed as multiple flow integrals of the two-, three- and four-point functions of the trace of the stress tensor. Eliminating $\Delta a’$,... read more

## 01A1 D. Anselmi A universal flow invariant in quantum field theory

A flow invariant is a quantity depending only on the UV and IR conformal fixed points and not on the flow connecting them. Typically, its value is related to the central charges a and c. In classically-conformal field theories, scale invariance is broken by quantum effects and the flow invariant... read more

## 00A1 D. Anselmi Large-N expansion, conformal field theory and renormalization-group flows in three dimensions

I study a class of interacting conformal field theories and conformal windows in three dimensions, formulated using the Parisi large-$N$ approach and a modified dimensional-regularization technique. Bosons are associated with composite operators and their propagators are dynamically generated by fermion bubbles. Renormalization-group flows between pairs of interacting fixed points satisfy... read more

## 99A6 D. Anselmi Irreversibility and higher-spin conformal field theory

I discuss the properties of the central charges $c$ and $a$ for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but... read more

## 99A5 D. Anselmi Exact results on quantum field theories interpolating between pairs of conformal field theories

I review recent results on conformal field theories in four dimensions and quantum field theories interpolating between conformal fixed points, supersymmetric and non-supersymmetric. The talk is structured in three parts: $i$) central charges, $ii$) anomalous dimensions and $iii$) quantum irreversibility.

PDF

PoS (trieste99) 013

arXiv:hep-th/9910255

## 99A4 D. Anselmi Towards the classification of conformal field theories in arbitrary even dimension

I identify the class of even-dimensional conformal field theories that is most similar to two-dimensional conformal field theory. In this class the formula, elaborated recently, for the irreversibility of the renormalization-group flow applies also to massive flows. This implies a prediction for the ratio between the coefficient of the Euler... read more

## 99A3 D. Anselmi Higher-spin current multiplets in operator-product expansions

Various formulas for currents with arbitrary spin are worked out in general space-time dimension, in the free field limit and, at the bare level, in presence of interactions. As the n-dimensional generalization of the (conformal) vector field, the $(n/2-1)$-form is used. The two-point functions and the higher-spin central charges are... read more

## 99A2 D. Anselmi Quantum irreversibility in arbitrary dimension

Some recent ideas are generalized from four dimensions to the general dimension $n$. In quantum field theory, two terms of the trace anomaly in external gravity, the Euler density $G_n$ and $\Box^{n/2-1}R$, are relevant to the problem of quantum irreversibility. By adding the divergence of a gauge-invariant current, $G_n$ can... read more

## 99A1 D. Anselmi Anomalies, unitarity and quantum irreversibility

The trace anomaly in external gravity is the sum of three terms at criticality: the square of the Weyl tensor, the Euler density and $\Box R$, with coefficients, properly normalized, called $c$, $a$ and $a’$, the latter being ambiguously defined by an additive constant. Considerations about unitarity and positivity properties... read more

## 98A3 D. Anselmi Quantum Conformal Algebras and Closed Conformal Field Theory

We investigate the quantum conformal algebras of N=2 and N=1 supersymmetric gauge theories. Phenomena occurring at strong coupling are analysed using the Nachtmann theorem and very general, model-independent, arguments. The results lead us to introduce a novel class of conformal field theories, identified by a closed quantum conformal algebra. We... read more

## 98A2 D. Anselmi The N=4 Quantum Conformal Algebra

We determine the spectrum of currents generated by the operator product expansion of the energy-momentum tensor in N=4 super-symmetric Yang-Mills theory. Up to the regular terms and in addition to the multiplet of the stress tensor, three current multiplets appear, Sigma, Xi and Upsilon, starting with spin 0, 2 and... read more

## 98A1 D. Anselmi Theory of higher spin tensor currents and central charges

We study higher spin tensor currents in quantum field theory. Scalar, spinor and vector fields admit unique “improved” currents of arbitrary spin, traceless and conserved. Off-criticality as well as at interacting fixed points conservation is violated and the dimension of the current is anomalous. In particular, currents $J^{(s,I)}$ with spin... read more

## 97A1 D. Anselmi Central functions and their physical implications

Central functions $c(g)$ and $c'(g)$ are constructed in quantum field theory. These quantities justify and generalize the notions of central charges recently introduced at criticality, which, together with suitable anomalous dimensions $h$, identify a conformal field theory in four dimensions (CFT$_4$). They are encoded in the four-point function of the stress-energy tensors. The... read more

## 96A1 D. Anselmi Quantum topological invariants, gravitational instantons and the topological embedding

Certain topological invariants of the moduli space of gravitational instantons are defined and studied. Several amplitudes of two and four dimensional topological gravity are computed. A notion of puncture in four dimensions, that is particularly meaningful in the class of Weyl instantons, is introduced. The topological embedding, a theoretical framework... read more

## 95A2 D. Anselmi On field theory quantization around instantons

With the perspective of looking for experimentally detectable physical applications of the so-called topological embedding, a procedure recently proposed by the author for quantizing a field theory around a non-discrete space of classical minima (instantons, for example), the physical implications are discussed in a “theoretical” framework, the ideas are collected... read more

## 95A1 D. Anselmi Topological field theory and physics

Topological Yang-Mills theory with the Belavin-Polyakov-Schwarz-Tyupkin $SU(2)$ instanton is solved completely, revealing an underlying multi-link intersection theory. Link invariants are also shown to survive the coupling to a certain kind of matter (hyperinstantons). The physical relevance of topological field theory and its invariants is discovered. By embedding topological Yang-Mills theory... read more

## 94A2 D. Anselmi Anomalies in instanton calculus

I develop a formalism for solving topological field theories explicitly, in the case when the explicit expression of the instantons is known. I solve topological Yang-Mills theory with the $k=1$ Belavin et al. instanton and topological gravity with the Eguchi-Hanson instanton. It turns out that naively empty theories are indeed... read more

## 94A1 D. Anselmi More on the subtraction algorithm

We go on in the program of investigating the removal of divergences of a generical quantum gauge field theory, in the context of the Batalin-Vilkovisky formalism. We extend to open gauge-algebrae a recently formulated algorithm, based on redefinitions $\delta\lambda$ of the parameters $\lambda$ of the classical Lagrangian and canonical transformations,... read more

## 93A2 D. Anselmi Removal of divergences with the Batalin-Vilkovisky formalism

We consider the problem of removing the divergences in an arbitrary gauge-field theory (possibly nonrenormalizable). We show that this can be achieved by performing, order by order in the loop expansion, a redefinition of some parameters (possibly infinitely many) and a canonical transformation (in the sense of Batalin and Vilkovisky)... read more

## 93A1 D. Anselmi Covariant Pauli-Villars regularization of quantum gravity at the one loop order

We study a regularization of the Pauli-Villars kind of the one loop gravitational divergences in any dimension. The Pauli-Villars fields are massive particles coupled to gravity in a covariant and nonminimal way, namely one real tensor and one complex vector. The gauge is fixed by means of the unusual gauge-fixing... read more

Quantum Gravity

### Book

14B1 D. Anselmi
Renormalization

Course on renormalization, taught in Pisa in 2015. (More chapters will be added later.)

Last update: May 9th 2015, 230 pages

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Contents:
Preface
1. Functional integral
2. Renormalization
3. Renormalization group
4. Gauge symmetry
5. Canonical formalism
6. Quantum electrodynamics
7. Non-Abelian gauge field theories
Notation and useful formulas
References

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