Searcharxiv⌕ Search

arXiv subjects

Peter M. Lavrov

Publications and source records attributed to Peter M. Lavrov.

At least 19 recordsLinked to original sources
arXiv2022

BRST, Ward identities, gauge dependence, and a functional renormalization group

Basic properties of gauge theories in the framework of Faddeev-Popov (FP) method, Batalin-Vilkovisky (BV) formalism, functional renormalization group (FRG) approach are considered. The FP and BV quantizations are characterized by the Becchi-Rouet-Stora-Tyutin (BRST) symmetry while the BRST symmetry is broken in the FRG approach. It is shown that the FP method, the BV formalism and the FRG approach can be provided with the Slavnov-Taylor identity, the Ward identity and the modified Slavnov-Taylor identity, respectively. It is proven that using the background field method the background gauge invariance of effective action within the FP and FRG quantization procedures can be achieved in nonlinear gauges. The gauge-dependence problem within the FP, BV and FRG quantizations is studied. Arguments allowing us to state the existence of principal problems of the FRG in the case of gauge theories are given.

hep-th↗
arXiv2021

Gauge dependence of effective average action

The gauge dependence of effective average action in the functional renormalization group is studied. The effective average action is considered as non-perturbative solution to the flow equation which is the basic equation of the method. It is proven that at any scale of IR cutoff the effective average action depends on gauges making impossible physical interpretation of all obtained results in this method.

hep-th↗
arXiv2020

Gauge dependence of alternative flow equation for the functional renormalization group

The gauge dependence problem of alternative flow equation for the functional renormalization group is studied. It is shown that the effective two-particle irreducible effective action depends on gauges at any value of IR parameter $k$. The situation with gauge dependence is similar to the standard formulation based on the effective one-particle irreducible effective action.

hep-th↗
arXiv2020

Functional renormalization group approach and gauge dependence in gravity theories

We investigate the gauge symmetry and gauge fixing dependence properties of the effective average action for quantum gravity models of general form. Using the background field formalism and the standard BRST-based arguments, one can establish the special class of regulator functions that preserves the background field symmetry of the effective average action. Unfortunately, regardless the gauge symmetry is preserved at the quantum level, the non-invariance of the regulator action under the global BRST transformations leads to the gauge fixing dependence even under the use of the on-shell conditions.

hep-th↗
arXiv2020

RG and BV-formalism

In present paper a quantization scheme proposed recently by Morris (arXiv:1806.02206[hep-th]) is analyzed. This method is based on idea to combine the renormalization group with the BV-formalism in an unique quantization procedure. It is shown that the BV-formalism and the new method should be considered as independent approaches to quantization of gauge systems both provided by global supersymmetry.

hep-th↗
arXiv2020

Multiplicative renormalizability of Yang-Mills theory with the background field method in the BV-formalism

Studying the gauge-invariant renormalizability of four-dimensional Yang-Mills theory using the background field method and the BV-formalism, we derive a classical master-equation homogeneous with respect to the antibracket by introducing antifield partners to the background fields and parameters. The constructed model can be renormalized by the standard method of introducing counterterms. This model does not have (exact) multiplicative renormalizability but it does have this property in the physical sector (quasimultiplicative renormalizability).

hep-th↗
arXiv2019

Background field method and nonlinear gauges

We present a reformulation of the background field method for Yang-Mills type theories, based on using a superalgebra of generators of BRST and background field transformations. The new approach enables one to implement and consistently use non-linear gauges in a natural way, by using the requirement of invariance of the fermion gauge-fixing functional under the background field transformations.

hep-th↗
arXiv2019

Gauge invariance of the background average effective action

Using the background field method for the functional renormalization group approach in the case of a generic gauge theory, we study the background field symmetry and gauge dependence of the background average effective action, when the regulator action depends on external fields. The final result is that the symmetry of the average effective action can be maintained for a wide class of regulator functions, but in all cases the dependence of the gauge fixing remains on-shell. The Yang-Mills theory is considered as the main particular example.

hep-th↗
arXiv2019

Gauge dependence and multiplicative renormalization of Yang-Mills theory with matter fields

In the paper, within the background field method, the renormalization and the gauge dependence is studied as for an SU(2) Yang-Mills theory with multiplets of spinor and scalar fields. By extending the quantum action of the BV-formalism with an extra fermion vector field and a constant fermion parameter, the multiplicative character of the renormalizability is proven. The renormalization of all the physical parameters of the theory under consideration is shown to be gauge-independent.

hep-th↗
arXiv2019

Gauge invariant renormalizability of quantum gravity

Using the Batalin-Vilkovisky technique and the background field method the proof of gauge invariant renormalizability is elaborated for a generic model of quantum gravity which is diffeomorphism invariant and has no other, potentially anomalous, symmetries. The gauge invariant renormalizability means that in all orders of loop expansion of the quantum effective action one can control deformations of the generators of gauge transformations which leave such an action invariant. In quantum gravity this means that one can maintain general covariance of the divergent part of effective action when the mean quantum field, ghosts and antifields are switched off.

hep-th↗
arXiv2019

Gauge (in)dependence and background field formalism

It is shown that the gauge invariance and gauge dependence properties of effective action for Yang-Mills theories should be considered as two independent issues in the background field formalism. Application of this formalism to formulate the functional renormalization group approach is discussed. It is proven that there is a possibility to construct the corresponding average effective action invariant under the gauge transformations of background vector field. Nevertheless, being gauge invariant this action remains gauge dependent on-shell.

hep-th↗
arXiv2018

Quantum Gravity and background field formalism

We analyze the problem of general covariance for quantum gravity theories in the background field formalism with respect to gauge fixing procedure. We prove that the background effective action is not invariant under general coordinate transformations of background metric tensor in non-linear gauges.

hep-th↗
arXiv2018

General conversion method for constrained systems

We reformulate in a systematic way the conversional approach in its most general and compact form. We present a new definition of generalized Dirac bracket directly in terms of the super-observables commuting with the basic BFV-BRST charge.

hep-th↗
arXiv2018

Multiplicative renormalization of Yang-Mills theories in the background-field formalism

In the paper, within the background-field method, the structure of renormalizations is studied as for Yang-Mills fields interacting with a multiplet of spinor fields. By extending the Faddeev-Popov action with extra fields and parameters, one is allowed to establish the multiplicative character of the renormalizability. The renormalization of the physical parameters is shown to be gauge-independent.

hep-th↗
arXiv2018

Quantum antibrackets: polarization and parametrization

By proceeding from a simple non-polarized formalism, we consider in detail the polarization procedure as applied to the generating equations of the quantum antibracket algebra, in terms of the parametrized generating operator.

hep-th↗
arXiv2017

On quantum-mechanical equations of motion in representation dependent of external sources

In the present paper, we consider in detail the aspects of the Heisenberg's equations of motion, related to their transformation to the representation dependent of external sources. We provide with a closed solution as to the variation-derivative motion equations in the general case of a normal form (symbol) chosen. We show that the action in the path integral does depend actually on a particular choice of a normal symbol. We have determined both the aspects of the latter dependence: the specific boundary conditions for virtual trajectories, and the specific boundary terms in the action.

hep-th↗
arXiv2017

Does the nontrivially deformed field-antifield formalism exist?

We reformulate the Lagrange deformed field-antifield BV -formalism suggested, in terms of the general Euler vector field $N$ generated by the antisymplectic potential. That $N$ generalizes, in a natural anticanonically-invariant manner, the usual power-counting operator. We provide for the "usual" gauge-fixing mechanism as applied to the deformed BV -formalism.

hep-th↗