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)
Functional integral
We develop a general fieldcovariant 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 oneparticle irreducible diagrams and upgrades the usual $\Gamma$functional in several respects. The functional $\Omega$ is determined from its classical limit applying the usual diagrammatic rules to the proper fields. Moreover, it behaves as a scalar under the most general perturbative field redefinitions, which can be expressed as linear transformations of the proper fields. We extend the BatalinVilkovisky formalism and the master equation. The master functional satisfies the extended master equation and behaves as a scalar under canonical transformations. The most general perturbative field redefinitions and changes of gaugefixing can be encoded in proper canonical transformations, which are linear and do not mix integrated fields and external sources. Therefore, they can be applied as true changes of variables in the functional integral, instead of mere replacements of integrands. This property overcomes a major difficulty of the functional $\Gamma$. Finally, the new approach allows us to prove the renormalizability of gauge theories in a general fieldcovariant setting. We generalize known cohomological theorems to the master functional and show that when there are no gauge anomalies all divergences can be subtracted by means of parameter redefinitions and proper canonical transformations.
Eur. Phys. J. C 73 (2013) 2363  DOI: 10.1140/epjc/s1005201323634
We study a new generating functional of oneparticle 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 transform as a scalar under an unusual transformation law. The master functional, on the other hand, is the Legendre transform of an improved functional W = ln Z with respect to the sources coupled to both elementary and composite fields. The inclusion of certain improvement terms in W and Z is necessary to make this transform well defined. The master functional behaves as a scalar under the transformation law inherited from its very definition. Moreover, it admits a proper formulation, obtained extending the set of integrated fields to the socalled proper fields, which allows us to work without passing through Z, W or $\Gamma$. In the proper formulation the classical action coincides with the classical limit of the master functional, and correlation functions and renormalization are calculated applying the usual diagrammatic rules to the proper fields. Finally, the most general change of field variables, including the map relating bare and renormalized fields, is a linear redefinition of the proper fields.
Eur. Phys. J. C 73 (2013) 2385  DOI: 10.1140/epjc/s100520132385y
Consider a functional integral
\[
\mathcal{I}=\int [\mathrm{d}\varphi ]\hspace{0.02in}\exp \left( S(\varphi)+\int J\left( \varphi bU\right) \right) ,
\]
where $U(\varphi ,bJ)$ is a local function of $\varphi$ and $J$, and $b$ is a constant. Then there exists a perturbatively local change of variables
\[
\varphi =\varphi (\varphi ^{\prime },b,bJ)=\varphi ^{\prime }+\mathcal{O}(b),
\]
expressed as a series expansion in $b$, such that
\[
\mathcal{I}=\int [\mathrm{d}\varphi ^{\prime }]\hspace{0.02in}\exp \left(
S^{\prime }(\varphi ^{\prime },b)+\int J\varphi ^{\prime }\right) ,
\]
where $S^{\prime }(\varphi ^{\prime },b)=S(\varphi (\varphi^{\prime },b,0))$.
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, or generating functionals before and after nonlinear changes of field variables. In this paper we investigate this issue and work out a general fieldcovariant approach to quantum field theory, which allows us to treat all perturbative changes of field variables, including the relation between bare and renormalized fields, as true changes of variables in the functional integral, under which the functionals Z and W = ln Z behave as scalars. We investigate the relation between composite fields and changes of field variables, and show that, if J are the sources coupled to the elementary fields, all changes of field variables can be expressed as Jdependent redefinitions of the sources L coupled to the composite fields. We also work out the relation between the renormalization of variablechanges and the renormalization of composite fields. Using our transformation rules it is possible to derive the renormalization of a theory in a new variable frame from the renormalization in the old variable frame, without having to calculate it anew. We define several approaches, useful for different purposes, in particular a linear approach where all variable changes are described as linear source redefinitions. We include a number of explicit examples.
Eur. Phys. J. C 73 (2013) 2338  DOI: 10.1140/epjc/s1005201323385
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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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