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

18A3 Damiano Anselmi and Marco Piva
Quantum gravity, fakeons and microcausalityWe investigate the properties of fakeons in quantum gravity at one loop. The theory is described by a graviton multiplet, which contains the fluctuation $h_{\mu ... (read more)

18A2 Damiano Anselmi and Marco Piva
The ultraviolet behavior of quantum gravityA theory of quantum gravity has been recently proposed by means of a novel quantization prescription, which is able to turn the poles of the ... (read more)

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 equationsThe cutting equations are diagrammatic identities that are used to prove perturbative unitarity in quantum field theory. In this paper, we derive algebraic, upgraded versions ... (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)
Background field method
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
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
13A3 D. Anselmi
Background field method, BatalinVilkovisky formalism and parametric completeness of renormalization
We investigate the background field method with the BatalinVilkovisky 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 transformations, we prove parametric completeness without making use of cohomological theorems, namely show that if the starting classical action is sufficiently general all divergences can be subtracted by means of parameter redefinitions and canonical transformations. Our approach applies to renormalizable and nonrenormalizable theories that are manifestly free of gauge anomalies and satisfy the following assumptions: the gauge algebra is irreducible and closes off shell, the gauge transformations are linear functions of the fields, and closure is fieldindependent. YangMills theories and quantum gravity in arbitrary dimensions are included, as well as effective and higherderivative versions of them, but several other theories, such as supergravity, are left out.
Phys. Rev. D 89 (2014) 045004  DOI: 10.1103/PhysRevD.89.045004
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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 (8)
 Fakeons (3)
 Renormalization of general gauge theories (14)
 Fieldcovariant quantum field theory (4)
 AdlerBardeen theorem (5)
 Quantum gravity (16)
 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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