Recent theorems

13T1 Theorem
Replacing fields with the solutions of their field equations preserves the master equation 
12T1 Theorem
Procedure to convert the functional integral to the conventional form 
06T1 Theorem
Terms quadratically proportional to the field equations and field redefinitions 
05T1 Theorem
Maximum poles of Feynman diagrams
Recent Papers

18A1 Damiano Anselmi
Fakeons and LeeWick modelsThe “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 ... (read more)

17A3 Damiano Anselmi
On the quantum field theory of the gravitational interactionsWe study the main options for a unitary and renormalizable, local quantum field theory of the gravitational interactions. The first model is a LeeWick superrenormalizable ... (read more)

17A2 Damiano Anselmi and Marco Piva
Perturbative unitarity of LeeWick quantum field theoryWe study the perturbative unitarity of the LeeWick models, formulated as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions ... (read more)

17A1 Damiano Anselmi and Marco Piva
A new formulation of LeeWick quantum field theoryThe LeeWick models are higherderivative theories that are claimed to be unitary thanks to a peculiar cancelation mechanism. In this paper, we provide a new ... (read more)

16A3 Damiano Anselmi
Algebraic cutting equationsWe prove a set of polynomial identities for complex numbers associated with Feynman diagrams. The equations are at the core of perturbative unitarity in quantum ... (read more)

16A2 Ugo G. Aglietti and Damiano Anselmi
Inconsistency of Minkowski higherderivative theoriesWe show that Minkowski higherderivative quantum field theories are generically inconsistent, because they generate nonlocal, nonHermitian ultraviolet divergences, which cannot be removed by means of ... (read more)

16A1 Damiano Anselmi
Aspects of perturbative unitarityWe reconsider perturbative unitarity in quantum field theory and upgrade several arguments and results. The minimum assumptions that lead to the largest time equation, the ... (read more)

15A4 Damiano Anselmi
Background field method and the cohomology of renormalizationUsing the background field method and the BatalinVilkovisky formalism, we prove a key theorem on the cohomology of perturbatively local functionals of arbitrary ghost numbers, ... (read more)

15A3 Damiano Anselmi
Some reference formulas for the generating functions of canonical transformationsWe study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating ... (read more)

15A2 Damiano Anselmi
AdlerBardeen theorem and cancellation of gauge anomalies to all orders in nonrenormalizable theoriesWe prove the AdlerBardeen theorem in a large class of general gauge theories, including nonrenormalizable ones. We assume that the gauge symmetries are general covariance, ... (read more)

15A1 Damiano Anselmi
Ward identities and gauge independence in general chiral gauge theoriesUsing the BatalinVilkovisky formalism, we study the Ward identities and the equations of gauge dependence in potentially anomalous general gauge theories, renormalizable or not. A ... (read more)

14A2 D. Anselmi
Weighted power counting and chiral dimensional regularizationWe define a modified dimensionalregularization technique that overcomes several difficulties of the ordinary technique, and is specially designed to work efficiently in chiral and parity ... (read more)

14A1 D. Anselmi
AdlerBardeen theorem and manifest anomaly cancellation to all orders in gauge theoriesWe reconsider the AdlerBardeen theorem for the cancellation of gauge anomalies to all orders, when they vanish at one loop. Using the BatalinVilkovisky formalism and ... (read more)

13A3 D. Anselmi
Background field method, BatalinVilkovisky formalism and parametric completeness of renormalizationWe investigate the background field method with the BatalinVilkovisky formalism, to generalize known results, study parametric completeness and achieve a better understanding of several properties. ... (read more)

13A2 D. Anselmi
Properties of the classical action of quantum gravityThe 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 ... (read more)
AdlerBardeen theorem
Using the background field method and the BatalinVilkovisky 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, nonAbelian YangMills 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.
Phys. Rev. D 93 (2016) 065034  DOI: 10.1103/PhysRevD.93.065034
15A2 Damiano Anselmi
AdlerBardeen theorem and cancellation of gauge anomalies to all orders in nonrenormalizable theories
We prove the AdlerBardeen 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 nonAbelian YangMills symmetries, and that the local functionals of vanishing ghost numbers satisfy a variant of the KlubergStern–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 finetuning local counterterms. The framework of the proof is worked out by combining a recently formulated chiral dimensional regularization with a gauge invariant higherderivative regularization. If the higherderivative regularizing terms are placed well beyond the truncation, and the energy scale $\Lambda $ associated with them is kept fixed, the theory is superrenormalizable 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.
Phys. Rev. D 91 (2015) 105016  DOI: 10.1103/PhysRevD.91.105016
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
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
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Book
14B1 D. Anselmi
Renormalization
Last update: May 9th 2015, 230 pages
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
Course on renormalization, taught in Pisa in 2015. (More chapters will be added later.)
Sections
 Unitarity of quantum field theory (6)
 Fakeons (1)
 Renormalization of general gauge theories (13)
 Fieldcovariant quantum field theory (4)
 AdlerBardeen theorem (5)
 Quantum gravity (15)
 Lorentz violating quantum field theory (8)
 Background field method (3)
 Infinite reduction of couplings (4)
 Renormalization group (14)
 Regularization (5)
 Conformal field theory (20)
 Topological field theory (5)
 Instantons (4)
 Field redefinitions (4)
 Dimensional regularization (5)
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