Course
19S1 D. Anselmi
Theories of gravitation
Program
Recent Papers

21A5 Damiano Anselmi
Diagrammar of physical and fake particles and spectral optical theoremWe prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman $i\epsilon $ prescription) and purely virtual particles (defined by ... (read 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 momentExtensions to the Standard Model that use strictly offshell degrees of freedom – the fakeons – allow for new measurable interactions at energy scales usually ... (read more)

21A3 Damiano Anselmi, Kristjan Kannike, Carlo Marzo, Luca Marzola, Aurora Melis, Kristjan Müürsepp, Marco Piva, Martti Raidal
Phenomenology of a Fake Inert Doublet ModelWe introduce a new way of modeling the physics beyond the Standard Model by considering fake, strictly offshell degrees of freedom: the fakeons. To demonstrate ... (read more)

21A2 Damiano Anselmi
Perturbation spectra and renormalizationgroup techniques in doublefield inflation and quantum gravity cosmologyWe 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 ... (read more)

21A1 Damiano Anselmi, Filippo Fruzza and Marco Piva
Renormalizationgroup techniques for singlefield inflation in primordial cosmology and quantum gravityWe study inflation as a “cosmic” renormalizationgroup flow. The flow, which encodes the dependence on the background metric, is described by a running coupling $\alpha ... (read more)

20A5 Damiano Anselmi
Highorder corrections to inflationary perturbation spectra in quantum gravityWe compute the inflationary perturbation spectra and the quantity $r+8n_{T}$ to the nexttonexttoleading log order in quantum gravity with purely virtual particles (which means the ... (read more)

20A4 Damiano Anselmi
Cosmic inflation as a renormalizationgroup flow: the running of power spectra in quantum gravityWe study the running of power spectra in inflationary cosmology as a renormalizationgroup flow from the de Sitter fixed point. The beta function is provided ... (read more)

20A3 Damiano Anselmi
Quantum field theories of arbitraryspin massive multiplets and Palatini quantum gravityWe formulate quantum field theories of massive fields of arbitrary spins. The presence of both physical and fake particles, organized into multiplets, makes it possible ... (read more)

20A2 Damiano Anselmi, Eugenio Bianchi and Marco Piva
Predictions of quantum gravity in inflationary cosmology: effects of the Weylsquared termWe derive the predictions of quantum gravity with fakeons on the amplitudes and spectral indices of the scalar and tensor fluctuations in inflationary cosmology. The ... (read more)

20A1 Damiano Anselmi
The quest for purely virtual quanta: fakeons versus FeynmanWheeler particlesThe search for purely virtual quanta has attracted interest in the past. We consider various proposals and compare them to the concept of fake particle, ... (read more)

19A3 Damiano Anselmi and Antonio Marino
Fakeons and microcausality: light cones, gravitational waves and the Hubble constantThe concept of fake particle, or “fakeon”, allows us to make sense of quantum gravity as an ultraviolet complete theory, by renouncing causality at very ... (read more)

19A2 Damiano Anselmi
Fakeons, unitarity, massive gravitons and the cosmological constantWe give a simple proof of perturbative unitarity in gauge theories and quantum gravity using a special gauge that allows us to separate the physical ... (read more)

19A1 Damiano Anselmi
Fakeons and the classicization of quantum gravity: the FLRW metricUnder certain assumptions, it is possible to make sense of higher derivative theories by quantizing the unwanted degrees of freedom as fakeons, which are later ... (read more)

18A7 Damiano Anselmi
On the nature of the Higgs bosonSeveral 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 ... (read more)

18A6 Damiano Anselmi
Let the dice play GodWe define life as the amplification of quantum uncertainty up to macroscopic scales. A living being is any amplifier that achieves this goal. We argue ... (read more)
Dimensional regularization
15A1 Damiano Anselmi
Ward identities and gauge independence in general chiral gauge theories
Using the BatalinVilkovisky 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 AdlerBardeen theorem. We show that when we make a canonical transformation on the treelevel action, it is always possible to rerenormalize the divergences and refinetune 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 gaugefixing parameters, although the physical quantities remain gauge independent. We discuss nontrivial checks of highorder calculations based on gauge independence and determine how powerful they are.
Phys. Rev. D 92 (2015) 025027  DOI: 10.1103/PhysRevD.92.025027
14B1 Damiano 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
 1.1 Path integral
 Schroedinger equation
 Free particle
 1.2 Free field theory
 1.3 Perturbative expansion
 Feynman rules
 1.4 Generating functionals, SchwingerDyson 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 CallanSymanzik 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 NonAbelian global symmetry
 4.4 NonAbelian 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 NonAbelian gauge field theories
 7.1 Renormalizability of nonAbelian gauge theories to all orders
 Raw subtraction
A. Notation and useful formulas
We define a modified dimensionalregularization 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 higherderivative 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 AdlerBardeen theorem. The difficulty of explicit computations, on the other hand, may increase.
Phys. Rev. D 89 (2014) 125024  DOI: 10.1103/PhysRevD.89.125024
14A1 D. Anselmi
AdlerBardeen theorem and manifest anomaly cancellation to all orders in gauge theories
We reconsider the AdlerBardeen theorem for the cancellation of gauge anomalies to all orders, when they vanish at one loop. Using the BatalinVilkovisky formalism and combining the dimensionalregularization technique with the higherderivative 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 orderbyorder 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.
Eur. Phys. J. C 74 (2014) 3083  DOI: 10.1140/epjc/s1005201430830
05T1 Theorem
Maximum poles of Feynman diagrams
The maximum pole of a diagram with $V$ vertices and $L$ loops is at most $1/\varepsilon^{m(V,L)}$, where $m(V,L)=\min (V1,L).$ The result holds in dimensional regularization, where $\varepsilon = dD$, $d$ is the physical dimension and $D$ the continued one. Moreover, vertices are counted treating mass terms and the other nondominant quadratic terms as “twoleg vertices”.
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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
Avaibable on Amazon:
Contents:
Preface
1. Functional integral
2. Renormalization
3. Renormalization group
4. Gauge symmetry
5. Canonical formalism
6. Quantum electrodynamics
7. NonAbelian gauge field theories
Notation and useful formulas
References
Sections
 Cosmology (11)
 Phenomenology beyond SM (3)
 Quantum gravity (50)
 Standard model (7)
 AdlerBardeen theorem (5)
 Background field method (3)
 Unitarity of quantum field theory (19)
 Fakeons (37)
 Renormalization of general gauge theories (14)
 Fieldcovariant quantum field theory (4)
 Lorentz violating quantum field theory (11)
 Renormalization group (14)
 Infinite reduction of couplings (5)
 Regularization (5)
 Conformal field theory (20)
 Topological field theory (5)
 Instantons (4)
 Field redefinitions (4)
 Dimensional regularization (5)
 Philosophy of science (6)
 Biophysics (3)
 Videos (20)
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