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Alexander A. Reshetnyak

Publications and source records attributed to Alexander A. Reshetnyak.

33 records · Page 2Linked to original sources
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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arXiv2015

Gauge dependence of vacuum expectation values of gauge invariant operators from soft breaking of BRST symmetry. Example of Gribov-Zwanziger action

We review the study of influence of the so-called soft BRST symmetry breaking within the Batalin-Vilkovisky (BV) formalism introduced in our papers [JHEP 1110 (2011) 043, arXiv:1108.4820 [hep-th], MPLA 27 (2012) 1250067, arXiv:1201.4720 [hep-th]] on gauge dependence of the effective action and vacuum expectation values of gauge invariant operators. We derive the Ward identities for generating functionals of Green's functions for a given theory with soft BRST symmetry breaking term being added to the quantum action and investigate theirs gauge dependence. It is strongly argued that gauge theories with a soft breaking of BRST symmetry are inconsistent within the BV formalism because of the gauge-dependence of $S$-matrix. The application to the Gribov-Zwanziger action (enlarging SU(N) Yang-Mills gauge theory by means of not gauge-invariant horizon function) for the one-parameter family of $R_ξ$ gauges with use of the new form of the Hermitian augmented Faddeev-Popov operator (being by Faddeev-Popov operator for transverse components of Yang--Mills fields) is considered.

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arXiv2014

On Consistent Lagrangian Quantization of Yang--Mills Theories without Gribov Copies

We review the results of our research [A.A. Reshetnyak, IJMPA 29 (2014) 1450184; P.Yu. Moshin, A.A. Reshetnyak, Nucl. Phys. B 888 (2014) 92; P.Yu. Moshin, A.A. Reshetnyak, Phys. Lett. B 739 (2014) 110; P.Yu. Moshin, A.A. Reshetnyak, arXiv:1406.5086[hep-th]], devoted to Lagrangian quantization for gauge theories with soft BRST symmetry breaking, in particular, for various descriptions of the YM theory without Gribov copies. The cited works rely on finite BRST and BRST-antiBRST transformations, respectively, with a singlet $Λ$ and a doublet $λ_{a}$, $a=1,2$, of anticommuting Grassmann parameters, both global and field-dependent. It turns out that global finite BRST and BRST-antiBRST transformations form a 1-parametric and a 2-parametric Abelian supergroup, respectively. Explicit superdeterminants corresponding to these changes of variables in the partition function allow one to calculate precise changes of the respective gauge-fixing functional. These facts provide the basis for a proof of gauge independence of the corresponding path integral under respective BRST and BRST-antiBRST transformations. It is shown that the gauge independence becomes restored for path integrals with soft BRST and BRST-antiBRST symmetry breaking terms. In this case, the form of transformation parameters is found to induce a precise change of the gauge in the path integral, thus connecting two arbitrary $R_ξ$-like gauges in the average effective action. Finite field-dependent BRST-antiBRST transformations are used to solve (perturbatively) the Gribov problem in the Gribov--Zwanziger approach. A modification of the path integral for theories with a gauge group, being consistent with gauge invariance and providing a restriction of the integration measure to the first Gribov region with a non-vanishing Faddeev--Popov determinant, is suggested.

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arXiv2014

BRST-BFV Lagrangian Formulations for Higher Spin Fields subject to two-column Young Tableaux

The details of Lagrangian description of irreducible integer higher-spin representations of the Poincare group with an Young tableaux $Y[\hat{s}_1,\hat{s}_2]$ having $2$ columns are considered for Bose particles propagated on an arbitrary dimensional Minkowski space-time. The procedure is based, first, on using of an auxiliary Fock space generated by Fermi oscillators (antisymmetric basis), second, on construction of the Verma module and finding auxiliary oscillator realization for $sl(2)\oplus sl(2)$ algebra which encodes the second-class operator constraints subsystem in the HS symmetry superalgebra. Application of an BRST-BFV receipt permits to reproduce gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive mixed-antisymmetric bosonic fields of any spin with appropriate number of gauge and Stueckelberg fields. The general prescription possesses by the possibility to derive constrained Lagrangians with only BRST-invariant extended algebraic constraints which describes the Poincare group irreducible representations in terms of mixed-antisymmetric tensor fields with 2 group indices.

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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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arXiv2014

On Composite fields approach to Gribov copies elimination in Yang-Mills theories

We suggest a method of introducing the Gribov--Zwanziger horizon functional, $H$, for Yang--Mills theories by using the composite fields technique: $σ(ϕ)=H$. A different form of the same horizon functional in gauges $χ$ and $χ^{\prime }$ is taken into account via (gauged) field-dependent BRST transformations connecting quantum Yang--Mills actions in these gauges. We introduce generating functionals of Green's functions with composite fields and derive the corresponding Ward identities. A study of gauge dependence shows that the effective action in Yang--Mills theories with the composite field $H$ does not depend on the gauge on the extremals determined by the Yang--Mills fields $ϕ$ alone.

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arXiv2012

On Lagrangian formulations for arbitrary bosonic HS fields on Minkowski backgrounds

We review the details of unconstrained Lagrangian formulations for Bose particles propagated on an arbitrary dimensional flat space-time and described by the unitary irreducible integer higher-spin representations of the Poincare group subject to Young tableaux $Y(s_1,...,s_k)$ with $k$ rows. The procedure is based on the construction of Verma modules and finding auxiliary oscillator realizations for the symplectic $sp(2k)$ algebra which encodes the second-class operator constraints subsystem in the HS symmetry algebra. Application of an universal BRST approach reproduces gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive bosonic fields of any spin with appropriate number of auxiliary fields.

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arXiv2010

Towards Lagrangian formulations of mixed-symmetry Higher Spin Fields on AdS-space within BFV-BRST formalism

The spectrum of superstring theory on the $AdS_5 \times S_5$ Ramond-Ramond background in tensionless limit contains integer and half-integer higher-spin fields subject at most to two-rows Young tableaux $Y(s_1,s_2)$. We review the details of a gauge-invariant Lagrangian description of such massive and massless higher-spin fields in anti-de-Sitter spaces with arbitrary dimensions. The procedure is based on the construction of Verma modules, its oscillator realizations and of a BFV-BRST operator for non-linear algebras encoding unitary irreducible representations of AdS group.

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arXiv2007

On Lagrangian Formulation for Half-integer HS Fields within Hamiltonian BRST Approach

A recent progress in a gauge-invariant Lagrangian description of massive and massless half-integer higher-spin fields in AdS and Minkowski spaces is presented. The procedure is based on a BFV-BRST operator, encoding the initial conditions realized by constraints in a Fock space and extracting the higher-spin fields from unitary irreducible representations of the AdS (Poincare) group. The construction is applicable to higher-spin tensor fields with a multi-row Young tableaux.

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arXiv2005

The Effective Action for Superfield Lagrangian Quantization in Reducible Hypergauges

The rules of local superfield Lagrangian quantization in reducible non-Abelian hypergauge functions are formulated for an arbitrary gauge theory. The generating functionals of standard and vertex Green's functions which depend on the Grassmann variable $η$ via super(anti)fields and sources are constructed. The difference between the local quantum and the gauge fixing actions determines an almost Hamiltonian system such that translations with respect to $η$ along the solutions of this system define the superfield BRST transformations. The Ward identities are derived and the gauge independence of the S-matrix is proved.

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