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A. A. Reshetnyak

Publications and source records attributed to A. A. Reshetnyak.

At least 19 recordsLinked to original sources
arXiv2025

Nonlinear Operator Superalgebras and BFV-BRST Operators for Lagrangian Description of Mixed-symmetry HS Fields in AdS Spaces

We study the properties of nonlinear superalgebras $\mathcal{A}$ and algebras $\mathcal{A}_b$ arising from a one-to-one correspondence between the sets of relations that extract AdS-group irreducible representations $D(E_0,s_1,s_2)$ in AdS$_d$-spaces and the sets of operators that form $\mathcal{A}$ and $\mathcal{A}_b$, respectively, for fermionic, $s_i=n_i+{1/2}$, and bosonic, $s_i=n_i$, $n_i \in \mathbb{N}_0$, $i=1,2$, HS fields characterized by a Young tableaux with two rows. We consider a method of constructing the Verma modules $V_\mathcal{A}$, $V_{\mathcal{A}_b}$ for $\mathcal{A}$, $\mathcal{A}_b$ and establish a possibility of their Fock-space realizations in terms of formal power series in oscillator operators which serve to realize an additive conversion of the above (super)algebra ($\mathcal{A}$) $\mathcal{A}_b$, containing a set of 2nd-class constraints, into a converted (super)algebra $\mathcal{A}_{b{}c}$ = $\mathcal{A}_{b}$ + $\mathcal{A}'_b$ ($\mathcal{A}_c$ = $\mathcal{A}$ + $\mathcal{A}'$), containing a set of 1st-class constraints only. For the algebra $\mathcal{A}_{b{}c}$, we construct an exact nilpotent BFV--BRST operator $Q'$ having nonvanishing terms of 3rd degree in the powers of ghost coordinates and use $Q'$ to construct a gauge-invariant Lagrangian formulation (LF) for HS fields with a given mass $m$ (energy $E_0(m)$) and generalized spin $\mathbf{s}$=$(s_1,s_2)$. LFs with off-shell algebraic constraints are examined as well.

hep-th↗
arXiv2023

Consistent Lagrangians for irreducible interacting higher-spin fields with holonomic constraints

We study the aspects of constructing the interactions for the higher spin fields in the framework of BRST approach. The main object of such an approach is BRST operator acting in the appropriate Fock space and building on the base of constraints that define the irreducible higher spin representations. In its turn, the constrains are divided into differential and purely algebraic or holonomic. The necessary and sufficient conditions to derive the consistent Lagrangian formulations for irreducible interacting higher-spin fields within approach with incomplete BRST operator, where the algebraic constraints are not included into definition of the BRST operator but imposed "by hands" on the field and gauge parameter vectors, are considered. It is shown that in addition to that such constraints should (anti)commute with the BRST operator and annihilate the fields and gauge parameters Fock space vectors, they must form the Abelian (super)algebra both with the BRST operator above and with operators of cubic, quartic and etc. vertices. Only under the above conditions, the formulations with complete and incomplete BRST charges turn out to be equivalent and yield to the same interaction vertices in terms of irreducible fields.

hep-th↗
arXiv2022

General Cubic Interacting Vertex for Massless Integer Higher Spin Fields

We consider a massless higher spin field theory within the BRST approach and construct a general off-shell cubic vertex corresponding to irreducible higher spin fields of helicities $s_1, s_2, s_3$. Unlike the previous works on cubic vertices, which do not take into account of the trace constraints, we use the complete BRST operator, including the trace constraints that describe an irreducible representation with definite integer helicity. As a result, we generalize the cubic vertex found in [arXiv:1205.3131 [hep-th]] and calculate the new contributions to the vertex, which contain additional terms with a smaller number space-time derivatives of the fields as well as the terms without derivatives.

hep-th↗
arXiv2022

Towards the structure of a cubic interaction vertex for massless integer higher spin fields

The structure of a cubic Lagrangian vertex is clarified for irreducible fields of helicities $s_1, s_2, s_3$ in a $d$-dimensional Minkowski space. An explicit form of the operator $\mathcal{Z}_j$ entering the vertex in a non-multiplicative way (examined in arXiv:2105.12030[hep-th] for $j=1$) is obtained. The solution is found within the BRST approach with complete BRST operators, which contain all constraints corresponding to the conditions that extract the irreducible fields, including trace operators.

hep-th↗
arXiv2019

Towards a theory of flow stress in multimodal polycrystalline aggregates. Effects of dispersion hardening

We elaborate the recently introduced theory of flow stress, including yield strength, in polycrystalline materials under quasi-static plastic deformations, thereby extending the case of single-mode aggregates to multimodal ones in the framework of a two-phase model which is characterized by the presence of crystalline and grain-boundary phases. Both analytic and graphic forms of the generalized Hall-Petch relations are obtained for multimodal samples with BCC ($α$-phase Fe), FCC (Cu, Al, Ni) and HCP (Cu, Al, Ni) and HCP ($α$-Ti, Zr) crystalline lattices at $T=300K$ with different values of the grain-boundary (second) phase. The case of dispersion hardening due to a natural incorporation into the model of a third phase including additional particles of doping materials is considered. The maximum of yield strength and the respective extremal grain size of samples are shifted by changing both the input from different grain modes and the values at the second and third phases. We study the influence of multimodality and dispersion hardening on the temperature-dimensional effect for yield strength within the range of $150-350K$.

cond-mat.mtrl-sci↗
arXiv2019

BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields

We construct a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with the corresponding Young tableaux having two rows, on a basis of the BRST approach. Starting with a description of fermionic higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system. For this purpose, we find auxiliary representations of the constraint subsuperalgebra containing the subsystem of second-class constraints in terms of Verma modules. We propose a universal procedure of constructing gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive fermionic fields of any spin. No off-shell constraints for the fields and gauge parameters are used from the very beginning. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincare-group representation. To illustrate the general construction, we obtain a Lagrangian description of fermionic fields with generalized spin (3/2,1/2) and (3/2,3/2) on a flat background containing the complete set of auxiliary fields and gauge symmetries.

hep-th↗
arXiv2016

On finite $N=1,2$ BRST transformations: Jacobians and Standard Model with gauge-invariant Gribov horizon

We review the concept and properties of finite field-dependent BRST and BRST-antiBRST transformations introduced in 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, [arxiv:1604.03027 [hep-th]]) for gauge theories. Exact rules for calculating the Jacobian of a corresponding change of variables in the partition function are presented. Infrared peculiarities under $R_ξ$-gauges in the Yang--Mills theory and Standard Model are examined in a gauge-invariant way with an appropriate horizon functional and unaffected local $N=1,2$ BRST symmetries.

hep-th↗
arXiv2015

Transport properties of AB stacked (Bernal) bilayer graphene on and without substrate within 2- and 4-band approximations

We present the results of the calculations of longitudinal and Hall conductivities of AB-stacked bilayer graphene as a function of frequency, finite chemical potential, temperature both with and without magnetic fields on a base of 2- and 4-band effective models. The limited cases of the conductivities for direct current are derived. The relations being important for optoelectronic among Hall conductivities and Faraday, Kerr angles in the AB-bilayers samples in the electric and magnetic fields when the radiation passes across bilayer sheets on different kinds a substrate are obtained.

cond-mat.mes-hall↗
arXiv2012

Soft breaking of BRST symmetry and gauge dependence

We continue investigation of soft breaking of BRST symmetry in the Batalin-Vilkovisky (BV) formalism beyond regularizations like dimensional ones used in our previous paper [JHEP 1110 (2011) 043, arXiv:1108.4820 [hep-th]]. We generalize a definition of soft breaking of BRST symmetry valid for general gauge theories and arbitrary gauge fixing. The gauge dependence of generating functionals of Green's functions is investigated. It is proved that such introduction of a soft breaking of BRST symmetry into gauge theories leads to inconsistency of the conventional BV formalism.

hep-th↗
arXiv2009

Programming Realization of Symbolic Computations for Non-linear Commutator Superalgebras over the Heisenberg--Weyl Superalgebra: Data Structures and Processing Methods

We suggest a programming realization of an algorithm for verifying a given set of algebraic relations in the form of a supercommutator multiplication table for the Verma module, which is constructed according to a generalized Cartan procedure for a quadratic superalgebra and whose elements are realized as a formal power series with respect to non-commuting elements. To this end, we propose an algebraic procedure of Verma module construction and its realization in terms of non-commuting creation and annihilation operators of a given Heisenberg--Weyl superalgebra. In doing so, we set up a problem which naturally arises within a Lagrangian description of higher-spin fields in anti-de-Sitter (AdS) spaces: to verify the fact that the resulting Verma module elements obey the given commutator multiplication for the original non-linear superalgebra. The problem setting is based on a restricted principle of mathematical induction, in powers of inverse squared radius of the AdS-space. For a construction of an algorithm resolving this problem, we use a two-level data model within the object-oriented approach, which is realized on a basis of the programming language C#. The program allows one to consider objects (of a less general nature than non-linear commutator superalgebras) that fall under the class of so-called $GR$-algebras, for whose treatment one widely uses the module \emph{Plural} of the system \emph{Singular} of symbolic computations for polynomials.

hep-th↗
arXiv2008

On Lagrangian formulations for mixed-symmetry HS fields on AdS spaces within BFV-BRST approach

The key aspects of a gauge-invariant Lagrangian description of massive and massless half-integer higher-spin fields in AdS spaces with a two-row Young tableaux $Y(s_1,s_2)$ are presented in an unconstrained description, as well as in off-shell formulations with algebraic constraints, on the basis of BFV-BRST operators for non-linear operator superalgebras, encoding the initial conditions realized by constraints in a Fock space and extracting the higher-spin fields from unitary representations of the AdS group.

hep-th↗
arXiv2007

BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space

We develop a general gauge invariant Lagrangian construction for half-integer higher spin fields in the AdS space of any dimension. Starting with formulation in terms of auxiliary Fock space we derive the closed nonlinear symmetry algebras of higher spin fermionic fields in the AdS space and find the corresponding BRST operator. A universal procedure of constructing the gauge invariant Lagrangians describing the dynamics of fermionic fields of any spin is developed. No off-shell constraints for the fields and gauge parameters are imposed from the very beginning. It is shown that all the constraints determining the irreducible representation of the AdS group arise as a consequence of the equations of motion and gauge transformations. As an example of the general procedure, we derive the gauge invariant Lagrangians for massive fermionic fields of spin 1/2 and 3/2 containing the total set of auxiliary fields and gauge symmetries.

hep-th↗
arXiv2005

Local Superfield Lagrangian BRST Quantization

A $θ$-local formulation of superfield Lagrangian quantization in non-Abelian hypergauges is proposed on the basis of an extension of general reducible gauge theories to special superfield models with a Grassmann parameter $θ$. We solve the problem of describing the quantum action and the gauge algebra of an $L$-stage-reducible superfield model in terms of a BRST charge for a formal dynamical system with first-class constraints of $(L+1)$-stage reducibility. Starting from $θ$-local functions of the quantum and gauge-fixing actions, with an essential use of Darboux coordinates on the antisymplectic manifold, we construct superfield generating functionals of Green's functions, including the effective action. We present two superfield forms of BRST transformations, considered as $θ$-shifts along vector fields defined by Hamiltonian-like systems constructed in terms of the quantum and gauge-fixing actions and an arbitrary $θ$-local boson function, as well as in terms of corresponding fermion functionals, through Poisson brackets with opposite Grassmann parities. The gauge independence of the S-matrix is proved. The Ward identities are derived. Connection is established with the BV method, the multilevel Batalin-Tyutin formalism, as well as with the superfield quantization scheme of Lavrov, Moshin, and Reshetnyak, extended to the case of general coordinates.

hep-th↗
arXiv2005

An Embedding of the BV Quantization into an N=1 Local Superfield Formalism

We propose an N=1 superfield formulation of Lagrangian quantization in general hypergauges by extending a reducible gauge theory to a superfield model with a local dependence on a Grassmann parameter $θ$. By means of $θ$-local functions of the quantum and gauge-fixing actions in terms of Darboux coordinates on the antisymplectic manifold, we construct superfield generating functionals of Green's functions, including the effective action. We prove the gauge-independence of the S-matrix, obtain the Ward identities and establish a relation of the proposed local quantization with the BV method and the multilevel Batalin-Tyutin formalism.

hep-th↗
arXiv2004

Basic features of General Superfield Quantization Method for gauge theories in Lagrangian formalism

The rules for superfield Lagrangian quantization method for general gauge theories on a basis of their generalization to special superfield models within a so-called $θ$-superfield theory of fields ($θ$-STF) are formulated. The $θ$-superfield generating functionals of Green's functions together with effective action are constructed. Their properties including new interpretation and superfield realization of BRST transformations, Ward identities are studied.

hep-th↗
arXiv2003

General Superfield Quantization Method. I. Lagrangian Formalism of $θ$-Superfield Theory of Fields

The rules to construct Lagrangian formulation for $θ$-superfield theory of fields ($θ$-STF) are introduced and considered on the whole in the framework of new superfield quantization method for general gauge theories. Algebraic, group-theoretic and analytic description aspects for supervariables over (Grassmann) algebras containing anticommuting generating element $θ$ and interpreted further in particular as an "odd" time are examined. Superfunction $S_{L}(θ)$, its global symmetries are defined on the extended space $T_{odd}{\cal M}_{cl} \times \{θ\}$ parameterized by superfields ${\cal A}^{\imath}(θ), \frac{d{\cal A}^{\imath}(θ)}{dθ\phantom{xxx}}, θ$. Extremality properties of superfunctional $Z[{\cal A}]=\int dθS_{L}(θ)$ and ones of corresponding Euler-Lagrange equations are analyzed. The direct and inverse problems of zero locus reduction for extended (anti)symplectic manifolds over ${\cal M}_{min}$ = $\{({\cal A}^{\imath}(θ), C^α(θ))\}$, with (odd) even brackets, corresponding to initial $θ$-superfield models are employed to construct iteratively the new interconnected models both embedded into manifolds above with reduced brackets and enlarging them with continued ones. Component (on $θ$) formulation for $θ$-STF variables and operations is produced providing the connection with standard gauge field theory. Realization of $θ$-STF constructions is demonstrated on models of scalar, spinor, vector superfields which are used to formulate the $θ$-superfield model with abelian two-parametric gauge supergroup.

hep-th↗
arXiv2003

General Superfield Quantization Method. II. General Superfield Theory of Fields: Hamiltonian Formalism

In the framework of started in Ref.[1] construction procedure of the general superfield quantization method for gauge theories in Lagrangian formalism the rules for Hamiltonian formulation of general superfield theory of fields (GSTF) are introduced and are on the whole considered. Mathematical means developed in [1] for Lagrangian formulation of GSTF are extended to use in Hamiltonian one. Hamiltonization for Lagrangian formulation of GSTF via Legendre transform of superfunction $S_{L}\bigl({\cal A}(θ),{\stackrel{\circ}{\cal A}}(θ),θ\bigr)$ with respect to ${\stackrel{\circ}{{\cal A}^{\imath}}}(θ)$ is considered. As result on the space $T^{\ast}_{odd}{\cal M}_{cl}\times \{θ\}$ parametrized by classical superfields ${\cal A}^{\imath}(θ)$, superantifields ${\cal A}^{\ast}_{\imath}(θ)$ and odd Grassmann variable $θ$ the superfunction $S_{H}({\cal A}(θ),{\cal A}^{\ast}(θ),θ)$ is defined. Being equivalent to different types of Euler-Lagrange equations the distinct Hamiltonian systems are investigated. Translations along $θ$ for superfunctions on $T^{\ast}_{odd}{\cal M}_{cl}\times \{θ\}$ being associated with these systems are studied. Various types of antibrackets and differential operators acting on $C^{k}\bigl(T^{\ast}_{odd}{\cal M}_{cl} \times \{θ\} \bigr)$ are considered. Component (on $θ$)formulation for GSTF quantities and operations is produced. Analogy between ordinary Hamiltonian classical mechanics and GSTF in Hamiltonian formulation is proposed. Realization of the GSTF general scheme is demonstrated on 6 models.

hep-th↗