arXiv subjects

Pavel Yu. Moshin

Publications and source records attributed to Pavel Yu. Moshin.

11 recordsLinked to original sources

arXiv2022

Non-Abelian gauge theories with composite fields in the background field method

Non-Abelian gauge theories with composite fields are examined in the background field method. Generating functionals of Green's functions for a Yang--Mills theory with composite and background fields are introduced, including the generating functional of vertex Green's functions (effective action). The corresponding Ward identities are obtained, and the issue of gauge dependence is investigated. A gauge variation of the effective action is found in terms of a nilpotent operator depending on the composite and background fields. On-shell independence from the choice of gauge fixing for the effective action is established. In the study of the Ward identities and gauge dependence, finite field-dependent BRST transformations with a background field are introduced and utilized on a systematic basis. On the one hand, this involves the consideration of (modified) Ward identities with a field-dependent anticommuting parameter, also depending on a non-trivial background.On the other hand, the issue of gauge dependence is studied with reference to a finite variation of the gauge Fermion. The concept of a joint introduction of composite and background fields to non-Abelian gauge theories is exemplified by the Gribov--Zwanziger theory, including the case of a local BRST-invariant horizon, and by the Volovich--Katanaev model of two-dimensional gravity with dynamical torsion.

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arXiv2019

Field-dependent BRST-antiBRST Transformations in Yang-Mills and Gribov-Zwanziger Theories

We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet $λ_{a}$, $a=1,2$, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with $s_{a}$-potential parameters $λ_{a}=s_{a}Λ$ induced by a finite even-valued functional $Λ$ and by the anticommuting generators $s_{a}$ of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary $R_{ξ}$-like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional $h$, given in the Landau gauge, and being an additive extension of the Yang-Mills action by the Gribov horizon functional in the Gribov-Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST-antiBRST\ transformations to the case of general gauge theories and present an ansatz for such transformations.

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arXiv2017

Finite BRST Mapping in Higher Derivative Models

We continue the study of finite field dependent BRST (FFBRST) symmetry in the quantum theory of gauge fields. An expression for the Jacobian of path integral measure is presented, depending on a finite field-dependent parameter, and the FFBRST symmetry is then applied to a number of well-established quantum gauge theories in a form which includes higher-derivative terms. Specifically, we examine the corresponding versions of the Maxwell theory, non-Abelian vector field theory, and gravitation theory. We present a systematic mapping between different forms of gauge-fixing, including those with higher-derivative terms, for which these theories have better renormalization properties. In doing so, we also provide the independence of the S-matrix from a particular gauge-fixing with higher derivatives. Following this method, a higher-derivative quantum action can be constructed for any gauge theory in the FFBRST framework.

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arXiv2016

Comparative analysis of finite field-dependent BRST transformations

We present a review of our recent study (A. Reshetnyak, IJMPA 29 (2014) 1450128; P. Moshin, A. Reshetnyak, Nucl. Phys. B 888 (2014) 92; Phys. Lett B 739 (2014) 110; IJMPA 29 (2014) 1450159; IJMPA 30 (2015) 1550021; IJMPA 31 (2016) 1650111), in which the concept of finite field-dependent BRST and BRST-antiBRST transformations for gauge theories was introduced, and their properties investigated. An algorithm of exact calculation for the Jacobian of a respective change of variables in the path integral is presented. Applications to the Yang--Mills theory and Standard Model, in view of infra-red (Gribov) peculiarities, are discussed.

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arXiv2015

Finite Field-Dependent BRST-antiBRST Transformations: Jacobians and Application to the Standard Model

We continue our research Nucl.Phys B888, 92 (2014); Int. J. Mod. Phys. A29, 1450159 (2014); Phys. Lett. B739, 110 (2014); Int. J. Mod. Phys. A30, 1550021 (2015) and extend the class of finite BRST-antiBRST transformations with odd-valued parameters $λ_{a}$, $a=1,2$, introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST-antiBRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST-antiBRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST-antiBRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits non-trivial solutions leading to a Jacobian equal to unity. Finite BRST-antiBRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters $λ_{a}$ is obtained, providing the equivalence of path integrals in any $3$-parameter $R_{\boldsymbolξ}$-like gauges. The Gribov--Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in $R_{\boldsymbolξ}$-like gauges, in a gauge-independent way using field-dependent BRST-antiBRST transformations, and in $R_{\boldsymbolξ}$-like gauges using transverse-like non-Abelian gauge fields.

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arXiv2014

Finite BRST-antiBRST Transformations for the Theories with Gauge Group

Following our recent study [P.Yu. Moshin, A.A. Reshetnyak, Nucl. Phys. B 888 (2014) 92], we discuss the notion of finite BRST-antiBRST transformations, with a doublet $λ_{a}$, $a=1,2$, of anticommuting (both global and field-dependent) Grassmann parameters. It turns out that the global finite BRST-antiBRST transformations form a 2-parametric Abelian supergroup. We find an explicit Jacobian corresponding to this change of variables in the theories with a gauge group. Special field-dependent BRST-antiBRST transformations for the Yang--Mills path integral with $s_{a}$-potential (functionally-dependent) parameters $λ_{a}=s_{a}Λ$ generated by a finite even-valued functional $Λ$ and the anticommuting generators $s_{a}$ of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations and leads to the presence of modified Ward identities. The form of transformation parameters that induces a change of the gauge in the path integral is found and is exactly evaluated for connecting two arbitrary $R_ξ$-like gauges. The finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional $h_{ 0 }$, in the Landau gauge of the BRST-antiBRST setting in the Gribov--Zwanziger model, and to find $h_ξ$ corresponding to general $R_ξ$-like gauges in the form compatible with a gauge-independent $S$-matrix.

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arXiv2014

Finite BRST-antiBRST Transformations in Generalized Hamiltonian Formalism

We introduce the notion of finite BRST-antiBRST transformations for constrained dynamical systems in the generalized Hamiltonian formalism, both global and field-dependent, with a doublet $λ_{a}$, $a=1,2$, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in the path integral. It turns out that the finite transformations are quadratic in their parameters. Exactly as in the case of finite field-dependent BRST-antiBRST transformations for the Yang--Mills vacuum functional in the Lagrangian formalism examined in our previous paper [arXiv:1405.0790[hep-th]], special field-dependent BRST-antiBRST transformations with functionally-dependent parameters $λ_{a}=\int dt\(s_{a}Λ) $, generated by a finite even-valued function $Λ(t)$ and by the anticommuting generators $s_{a}$ of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing function for arbitrary constrained dynamical systems. This proves the independence of the vacuum functional under such transformations. We derive a new form of the Ward identities, depending on the parameters $λ_{a}$, and study the problem of gauge-dependence. We present the form of transformation parameters which generates a change of the gauge in the Hamiltonian path integral, evaluate it explicitly for connecting two arbitrary $R_ξ$-like gauges in the Yang--Mills theory and establish, after integration over momenta, a coincidence with the Lagrangian path integral [arXiv:1405.0790[hep-th]], which justifies the unitarity of the $S$-matrix in the Lagrangian approach.

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arXiv2014

Field-Dependent BRST-antiBRST Lagrangian Transformations

We continue our study of finite BRST-antiBRST transformations for general gauge theories in Lagrangian formalism, initiated in [arXiv:1405.0790[hep-th] and arXiv:1406.0179[hep-th]], with a doublet $λ_{a}$, $a=1,2$, of anticommuting Grassmann parameters and prove the correctness of the explicit Jacobian in the partition function announced in [arXiv:1406.0179[hep-th]], which corresponds to a change of variables with functionally-dependent parameters $λ_{a}=U_{a}Λ$ induced by a finite Bosonic functional $Λ(ϕ,π,λ)$ and by the anticommuting generators $U_{a}$ of BRST-antiBRST transformations in the space of fields $ϕ$ and auxiliary variables $π^{a},λ$. We obtain a Ward identity depending on the field-dependent parameters $λ_{a}$ and study the problem of gauge dependence, including the case of Yang--Mills theories. We examine a formulation with BRST-antiBRST symmetry breaking terms, additively introduced to the quantum action constructed by the Sp(2)-covariant Lagrangian rules, obtain the Ward identity and investigate the gauge-independence of the corresponding generating functional of Green's functions. A formulation with BRST symmetry breaking terms is developed. It is argued that the gauge independence of the above generating functionals is fulfilled in the BRST and BRST-antiBRST settings. These concepts are applied to the average effective action in Yang--Mills theories within the functional renormalization group approach.

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arXiv2014

Finite BRST-antiBRST Transformations in Lagrangian Formalism

We continue the study of finite BRST-antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [arXiv:1405.0790[hep-th]], with a doublet $λ_{a}$, $a=1,2$, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant $λ_{a}$. This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian [proved to be correct in [arXiv:1406.5086[hep-th]] for finite field-dependent BRST-antiBRST transformations with functionally-dependent parameters, $λ_{a}% =s_{a}Λ$, induced by a finite even-valued functional $Λ(ϕ,π,λ)$ and by the generators $s_{a}$ of BRST-antiBRST transformations acting in the space of fields $ϕ$, antifields $ϕ_{a}^{\ast}$, $\bar ϕ$ and auxiliary variables $π^{a},λ$. On the basis of this Jacobian, we solve a compensation equation for $Λ$, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities containing the parameters $λ_{a}$ and study the problem of gauge-dependence. The general approach is exemplified by the Freedman--Townsend model of\ a non-Abelian antisymmetric tensor field.

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arXiv2001

Gauge models in modified triplectic quantization

We apply the modified triplectic formalism for quantizing several popular gauge models - non-abelian antisymmetric tensor field model, W2-gravity and two-dimensional gravity with dynamical torsion. The explicit solutions are obtained for the generating equations of the quantum action and the gauge-fixing functional. Using these solutions we construct the vacuum functional and obtain the corresponding transformations of the extended BRST symmetry.

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arXiv1999

On gauge fixing in the Lagrangian formalism of superfield BRST quantization

We propose a modification of the gauge-fixing procedure in the Lagrangian method of superfield BRST quantization for general gauge theories which simultaneously provides a natural generalization of the well-known BV quantization scheme as far as gauge-fixing is concerned. A superfield form of BRST symmetry for the vacuum functional is found. The gauge-independence of the S-matrix is established.

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