Course

19S1 D. Anselmi
Theories of gravitation

Program

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Book

D. Anselmi
From Physics To Life

A journey to the infinitesimally small and back

In English and Italian

Available on Amazon:
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Recent Papers




Recent papers and theorems

24A2 Damiano Anselmi
Quantum gravity with purely virtual particles from asymptotically local quantum field theory

We investigate the local limits of various classes of unitary, nonlocal quantum field theories. While it is easy to build nonlocal models with well-behaved asymptotics in Euclidean space, the Minkowskian correlation functions typically exhibit singular behaviors. We introduce "asymptotically local" quantum field theory (AL-QFT) as the class that encompasses unitary, ... [more]

24A1 Damiano Anselmi
Cosmological inhomogeneities, primordial black holes, and a hypothesis on the death of the universe

We study the impact of the expansion of the universe on a broad class of objects, including black holes, neutron stars, white dwarfs, and others. Using metrics that incorporate primordial inhomogeneities, the effects of a hypothetical "center of the universe" on inflation are calculated. Dynamic coordinates for black holes that ... [more]

23A3 Damiano Anselmi
Gauge theories and quantum gravity in a finite interval of time, on a compact space manifold

We study gauge theories and quantum gravity in a finite interval of time $ \tau $, on a compact space manifold $\Omega $. The initial, final and boundary conditions are formulated in gauge invariant and general covariant ways by means of purely virtual extensions of the theories, which allow us ... [more]

23A2 Damiano Anselmi
Propagators and widths of physical and purely virtual particles in a finite interval of time

We study the free and dressed propagators of physical and purely virtual particles in a finite interval of time $τ$ and on a compact space manifold $Ω$, using coherent states. In the free-field limit, the propagators are described by the entire function $(e^{z}-1-z)/z^{2}$, whose shape on the real axis is ... [more]

23A1 Damiano Anselmi
Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity

We provide a diagrammatic formulation of perturbative quantum field theory in a finite interval of time $τ$, on a compact space manifold $Ω$. We explain how to compute the evolution operator $U(t_{\text{f}},t_{\text{i}})$ between the initial time $t_{\text{i}}$ and the final time $t_{\text{f}}=t_{\text{i}}+τ$, study unitarity and renormalizability, and show how to ... [more]

22A5 Damiano Anselmi
A new quantization principle from a minimally non time-ordered product

We formulate a new quantization principle for perturbative quantum field theory, based on a minimally non time-ordered product, and show that it gives the theories of physical particles and purely virtual particles. Given a classical Lagrangian, the quantization proceeds as usual, guided by the time-ordered product, up to the common ... [more]

22A4 Damiano Anselmi
Purely virtual extension of quantum field theory for gauge invariant fields: quantum gravity

Quantum gravity is extended to include purely virtual "cloud sectors", which allow us to define a complete set of point-dependent observables, including a gauge invariant metric and gauge invariant matter fields, and calculate their off-shell correlation functions perturbatively. The ordinary on-shell correlation functions and the $S$ matrix elements are unaffected. ... [more]

22A3 Damiano Anselmi
Purely virtual extension of quantum field theory for gauge invariant fields: Yang-Mills theory

We extend quantum field theory by including purely virtual "cloud" sectors, to define physical off-shell correlation functions of gauge invariant quark and gluon fields, without affecting the $S$ matrix amplitudes. The extension is made of certain cloud bosons, plus their anticommuting partners. Both are quantized as purely virtual, to ensure ... [more]

22R2 Damiano Anselmi
A hope for particle physics – ERC Advanced Grant application (VIRTUAL)

The physics of fundamental interactions is going through a concerning, prolonged period of stagnation. The incredible success of the standard model of particle physics and the lack of new experimental data have frustrated our hopes in the future. On top of that, the scientific community shattered into a large number ... [more]

22R1 Damiano Anselmi
Purely virtual particles in quantum gravity, inflationary cosmology and collider physics

We review the concept of purely virtual particle and its uses in quantum gravity, primordial cosmology and collider physics. The fake particle, or “fakeon”, which mediates interactions without appearing among the incoming and outgoing states, can be introduced by means of a new diagrammatics. The renormalization coincides with one of ... [more]

22A2 Damiano Anselmi
Purely virtual particles 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 ... [more]

22A1 Damiano Anselmi
Dressed 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 ... [more]

21A5 Damiano Anselmi
Diagrammar 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 ... [more]

21A4 Damiano Anselmi, Kristjan Kannike, Carlo Marzo, Luca Marzola, Aurora Melis, Kristjan Müürsepp, Marco Piva and Martti Raidal
A 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 ... [more]

21A3 Damiano Anselmi, Kristjan Kannike, Carlo Marzo, Luca Marzola, Aurora Melis, Kristjan Müürsepp, Marco Piva, Martti Raidal
Phenomenology 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. ... [more]

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, so that the correlation functions cannot be obtained as the analytic continuations of their Euclidean versions. The usual power counting rules fail and are replaced by much weaker ones. Self-energies generate complex divergences proportional to inverse powers of D’Alembertians. Three-point functions give more involved nonlocal divergences, which couple to infrared effects. The violations of the locality and Hermiticity of counterterms are illustrated by means of explicit computations in scalar models and higher-derivative gravity.

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Eur. Phys. J. C 77 (2017) 84 | DOI: 10.1140/epjc/s10052-017-4646-7

arXiv: 1612.06510 [hep-th]

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 gauge theories and generalize it to quantum gravity, in four and higher dimensions. The special gauge interpolates between the Feynman gauge and the Coulomb gauge without double poles. When the Coulomb limit is approached, the unphysical particles drop out of the cuts and the cutting equations are consistently projected onto the physical subspace. The proof does not extend to nonlocal quantum field theories of gauge fields and gravity, whose unitarity remains uncertain.

PDF

Phys. Rev. D 94 (2016) 025028 | DOI: 10.1103/PhysRevD.94.025028

arXiv: 1606.06348 [hep-th]

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 the background field approach and the usual, nonbackground approach by means of a canonical transformation, we take advantage of the properties of both approaches and prove that a closed functional is the sum of an exact functional plus a functional that depends only on the physical fields and possibly the ghosts. The assumptions of the theorem are the mathematical versions of general properties that characterize the counterterms and the local contributions to the potential anomalies. This makes the outcome a theorem on the cohomology of renormalization, rather than the whole local cohomology. The result supersedes numerous involved arguments that are available in the literature.

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Phys. Rev. D 93 (2016) 065034 | DOI: 10.1103/PhysRevD.93.065034

arXiv: 1511.01244 [hep-th]

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 to express the generating function of a canonical transformation by means of a certain “componential” map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.

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Eur. Phys. J. C 76 (2016) 49 | DOI: 10.1140/epjc/s10052-015-3874-y

arXiv: 1511.00828 [hep-th]

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. We show that if the gauge anomalies are trivial at one loop, for every truncation of the theory there exists a subtraction scheme where they manifestly vanish to all orders, within the truncation. Outside the truncation the cancellation of gauge anomalies can be enforced by fine-tuning local counterterms. The framework of the proof is worked out by combining a recently formulated chiral dimensional regularization with a gauge invariant higher-derivative regularization. If the higher-derivative regularizing terms are placed well beyond the truncation, and the energy scale $\Lambda $ associated with them is kept fixed, the theory is super-renormalizable and has the property that, once the gauge anomalies are canceled at one loop, they manifestly vanish from two loops onwards by simple power counting. When the $\Lambda $ divergences are subtracted away and $\Lambda $ is sent to infinity, the anomaly cancellation survives in a manifest form within the truncation and in a nonmanifest form outside. The standard model coupled to quantum gravity satisfies all the assumptions, so it is free of gauge anomalies to all orders.

PDF

Phys. Rev. D 91 (2015) 105016 | DOI: 10.1103/PhysRevD.91.105016

arXiv: 1501.07014 [hep-th]

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 ensures perturbative unitarity. Precisely, we consider potentially anomalous theories that are actually free of gauge anomalies thanks to the Adler-Bardeen theorem. We show that when we make a canonical transformation on the tree-level action, it is always possible to re-renormalize the divergences and re-fine-tune the finite local counterterms, so that the renormalized $\Gamma $ functional of the transformed theory is also free of gauge anomalies, and is related to the renormalized $\Gamma $ functional of the starting theory by a canonical transformation. An unexpected consequence of our results is that the beta functions of the couplings may depend on the gauge-fixing parameters, although the physical quantities remain gauge independent. We discuss nontrivial checks of high-order calculations based on gauge independence and determine how powerful they are.

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Phys. Rev. D 92 (2015) 025027 | DOI: 10.1103/PhysRevD.92.025027

arXiv: 1501.06692 [hep-th]

The properties of quantum gravity are reviewed from the point of view of renormalization. Various attempts to overcome the problem of nonrenormalizability are presented, and the reasons why most of them fail for quantum gravity are discussed. Interesting possibilities come from relaxing the locality assumption, which can inspire the investigation of a largely unexplored sector of quantum field theory. Another possibility is to work with infinitely many independent couplings, and search for physical quantities that only depend on a finite subset of them. In this spirit, it is useful to organize the classical action of quantum gravity, determined by renormalization, in a convenient way. Taking advantage of perturbative local field redefinitions, we write the action as the sum of the Hilbert term, the cosmological term, a peculiar scalar that is important only in higher dimensions, plus invariants constructed with at least three Weyl tensors. We show that the FRLW configurations, and many other locally conformally flat metrics, are exact solutions of the field equations in arbitrary dimensions $d>3$. If the metric is expanded around such configurations the quadratic part of the action is free of higher-time derivatives. Other well-known metrics, such as those of black holes, are instead affected in nontrivial ways by the classical corrections of quantum origin.

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Mod. Phys. Lett. A 30 (2015) 1540004 | DOI: 10.1142/S0217732315400040

Course on renormalization, taught in 2015.

Last update: September 15th 20123, 242 pages

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Contents:

Preface

1. Functional integral

  • 1.1 Path integral
    • Schroedinger equation
    • Free particle
  • 1.2 Free field theory
  • 1.3 Perturbative expansion
    • Feynman rules
  • 1.4 Generating functionals, Schwinger-Dyson equations
  • 1.5 Advanced generating functionals
  • 1.6 Massive vector fields
  • 1.7 Fermions

2. Renormalization

  • 2.1 Dimensional regularization
    • 2.1.1 Limits and other operations in $D$ dimensions
    • 2.1.2 Functional integration measure
    • 2.1.3 Dimensional regularization for vectors and fermions
  • 2.2 Divergences and counterterms
  • 2.3 Renormalization to all orders
  • 2.4 Locality of counterterms
  • 2.5 Power counting
  • 2.6 Renormalizable theories
  • 2.7 Composite fields
  • 2.8 Maximum poles of diagrams
  • 2.9 Subtraction prescription
  • 2.10 Regularization prescription
  • 2.11 Comments about the dimensional regularization
  • 2.12 About the series resummation

3. Renormalization group

  • 3.1 The Callan-Symanzik equation
  • 3.2 Finiteness of the beta function and the anomalous dimensions
  • 3.3 Fixed points of the RG flow
  • 3.4 Scheme (in)dependence
  • 3.5 A deeper look into the renormalization group

4. Gauge symmetry

  • 4.1 Abelian gauge symmetry
  • 4.2 Gauge fixing
  • 4.3 Non-Abelian global symmetry
  • 4.4 Non-Abelian gauge symmetry

5. Canonical gauge formalism

  • 5.1 General idea behind the canonical gauge formalism
  • 5.2 Systematics of the canonical gauge formalism
  • 5.3 Canonical transformations
  • 5.4 Gauge fixing
  • 5.5 Generating functionals
  • 5.6 Ward identities

6. Quantum electrodynamics

  • 6.1 Ward identities
  • 6.2 Renormalizability of QED to all orders

7 Non-Abelian gauge field theories

  • 7.1 Renormalizability of non-Abelian gauge theories to all orders
    • Raw subtraction

A. Notation and useful formulas

The PDF of the 2015 edition is available here below.

PDF

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 the components they have in the physical dimension, therefore the $\gamma $ matrices are the standard ones. Propagators are regularized with the help of evanescent higher-derivative kinetic terms, which are of the Majorana type in the case of chiral fermions. If the new terms are organized in a clever way, weighted power counting provides an efficient control on the renormalization of the theory, and allows us to show that the resulting chiral dimensional regularization is consistent to all orders. The new technique considerably simplifies the proofs of properties that hold to all orders, and makes them suitable to be generalized to wider classes of models. Typical examples are the renormalizability of chiral gauge theories and the Adler-Bardeen theorem. The difficulty of explicit computations, on the other hand, may increase.

PDF

Phys. Rev. D 89 (2014) 125024 | DOI: 10.1103/PhysRevD.89.125024

arXiv: 1405.3110 [hep-th]

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 matter in four dimensions, and identify the subtraction scheme where anomaly cancellation to all orders is manifest, namely no subtractions of finite local counterterms are required from two loops onwards. Our approach is based on an order-by-order analysis of renormalization, and, differently from most derivations existing in the literature, does not make use of arguments based on the properties of the renormalization group. As a consequence, the proof we give also applies to conformal field theories and finite theories.

PDF

Eur. Phys. J. C 74 (2014) 3083 | DOI: 10.1140/epjc/s10052-014-3083-0

arXiv: 1402.6453 [hep-th]

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Book

14B1 D. Anselmi
Renormalization

Course on renormalization, taught in 2015.

Last update: September 15th 2023, 242 pages

The final (2023) edition is vaibable on Amazon:

US  IT  DE  FR  ES  UK  JP  CA


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


The pdf file of the 2015 Edition is available here: PDF