arXiv subjects

Alexander A. Reshetnyak

Publications and source records attributed to Alexander A. Reshetnyak.

At least 19 recordsLinked to original sources

arXiv2026

On Lagrangian formulations for (ir)reducible mixed-antisymmetric higher integer spin fields in Minkowski spaces

We extend the results of Lagrangian formulations study to construct gauge-invariant Lagrangians for (ir)reducible integer higher-spin massless and massive representations of the Poincare group with a Young tableau $Y[\hat{s}_1,\hat{s}_2,\hat{s}_3]$ in $d$-dimensional flat space-time (as the probable candidates to describe the Dark Matter problem beyond the SM). These particles are described within a metric-like formulation by tensor fields with 3 groups of antisymmetric Lorentz indices $Φ_{μ^1[{\hat{s}_1}],μ^2[{\hat{s}_2}], μ^3[{\hat{s}_3}]}$ on a basis of the BRST method with complete, $Q$, and incomplete, $Q_c$, BRST operators. We found unconstrained (with $Q$) and constrained (with $Q_c$ and off-shell BRST invariant holonomic constraints) gauge Lagrangian formulations with different configuration spaces and reducibility stages. The deformation procedure to construct interacting gauge model with mixed-antisymmetric fields is proposed.

hep-th↗

arXiv2026

General Lagrangian formulations for mixed-antisymmetric tensor fields on flat backgrounds

Lagrangian formulations for (ir)reducible integer higher-spin massless and massive Poincare group representations subject to Young tableau with $k$ columns $Y[\hat{s}_1,\hat{s}_2,...,\hat{s}_k]$ in $d$-dimensional Minkowski space-time are firstly presented. The particles are described in a metric-like formulation by tensor fields with $k$ groups of antisymmetric Lorentz indices $Φ_{μ^1[{\hat{s}_1}],μ^2[{\hat{s}_2}],..., μ^k[{\hat{s}_k}]}$ by means of the BRST procedure with complete, $Q$, and incomplete, $Q_c$, BRST operators. Starting from a description of bosonic mixed-antisymmetric higher-spin fields in terms of an auxiliary Fock space associated with a special Poincare module, we realize a conversion of the initial operator constraint system into a system of first-class operator constraints. To this aim, we find, in first time, by means of Verma module the auxiliary representations of the constraint subalgebra, to be isomorphic due to Howe duality to $so(k,k)$ algebra, and containing the subsystem of second-class operators in terms of new oscillator variables forming the Fock module. An unconstrained (with $Q$) and constrained (with $Q_c$ and BRST invariant algebraic constraints) gauge Lagrangian formulations with equivalent dynamics, but different configuration spaces are found. Concept of consistent interactions are suggested.

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arXiv2025

General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. 2. Fermionic fields

We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having $k$ rows, on a basis of the BRST--BFV approach suggested for bosonic fields in our first article (Nucl. Phys. B862 (2012) 270, [arXiv:1110.5044[hep-th]). Starting from a description of fermionic mixed-symmetry higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with a special Poincare module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a system of first-class constraints. To do this, we find, in first time, by means of generalized Verma module the auxiliary representations of the constraint subsuperalgebra, to be isomorphic due to Howe duality to $osp(k|2k)$ superalgebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We suggest a universal procedure of finding unconstrained gauge-invariant Lagrangians with reducible gauge symmetries, describing the dynamics of both massless and massive fermionic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by constraints corresponding to an irreducible Poincare-group representation. As examples of the general approach, we propose a method of Lagrangian construction for fermionic fields subject to an arbitrary Young tableaux having 3 rows, and obtain a gauge-invariant Lagrangian for a new model of a massless rank-3 spin-tensor field of spin (5/2,3/2) with first-stage reducible gauge symmetries and a non-gauge Lagrangian for a massive rank-3 spin-tensor field of spin (5/2,3/2).

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arXiv2024

Covariant Lagrangian Cubic Interaction Vertices For Irreducible Higher Spin Fields in Minkowski Backgrounds

We review the application of BRST and BRST-BV approaches to construct the generic off-shell local Lorentz covariant cubic interaction vertices for irreducible massless and massive higher integer spin fields (as the candidates for massive particles in the Dark Matter problem) on $d$-dimensional Minkowski spaces. It is shown that equivalence among two Lagrangian dynamics for the same cubically interacting fields with given masses and spins obtained by means of the approach with complete BRST, $Q$, operator and of one with incomplete BRST, $Q_c$, operator in presence of consistent off-shell holonomic (traceless) constraints can be uplifted from the equivalence of the Lagrangians for free higher spin fields. We found that to get non-contradictory Lagrangians for irreducible interacting higher-spin fields within approach with $Q_c$ operator, together with off-shell algebraic constraints in addition to necessary condition of superconmmuting of $Q_c$ with appropriate holonomic constraints on the field and gauge parameter vectors, these constraints should form Abelian superalgebra both with BRST operator above and with operators of cubic vertices.

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arXiv2024

Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields

We develop the BRST approach to construct the general off-shell local Lorentz covariant cubic interaction vertices for irreducible massless and massive higher spin fields on $d$-dimensional Minkowski space. We consider two different cases for interacting higher spin fields: with one massive and two massless; with two massive both with coinciding and with different masses and one massless fields of spins $s_1, s_2, s_3$. Unlike the previous results on cubic vertices we extend our earlier result in [arXiv:2105.12030[hep-th]] for massless fields and employ the complete BRST operator, including the trace constraints that is used to formulate an irreducible representation with definite integer spin. We generalize the cubic vertices proposed for reducible higher spin fields in [arXiv:1205.3131 [hep-th]] in the form of multiplicative and non-multiplicative BRST-closed constituents and calculate the new contributions to the vertex, which contain additional terms with a smaller number space-time derivatives of the fields. We prove that without traceless conditions for the cubic vertices in [arXiv:1205.3131 [hep-th]] it is impossible to provide the noncontradictory Lagrangian dynamics and find explicit traceless solution for these vertices. As the examples, we explicitly construct the interacting Lagrangian for the massive of spin $s$ field and massless scalars both with and without auxiliary fields. The interacting models with different combinations of triples higher spin fields: massive of spin $s$ with massless scalar and vector fields and with two vector fields; massless of helicity $λ$ with massless scalar and massive vector fields; two massive fields of spins $s, 0$ and massless scalar are also considered.

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arXiv2023

Towards the Distribution of a Class of Polycrystalline Materials with an Equilibrium Defect Structure by Grain Diameters: Temperature Behavior of the Yield Strength

We modify a theory of flow stress introduced in [arXiv:1803.08247[cond-mat.mtrl-sci]], [arXiv:1809.03628[cond-mat.mes-hall]], [arXiv:1908.09338[cond-mat.mtrl-sci]] for a class of polycrystalline materials with equilibrium and quasy-equilibrium defect structure under quasi-static plastic deformations. We suggest, in addition to modified Bose-Einstein distribution, Maxwell-like distribution law for defects (within dislocation-disclination mechanism) in the grains of polycrystalline samples with respect to grain's diameter. Polycrystalline aggregates are considered within single- and two-phase models that correspond to the presence of crystalline and grain-boundary (porous) phases. The scalar dislocation density is derived. Analytic and graphic forms of the generalized Hall-Petch relations for yield strength are produced for single-mode samples with BCC ($α$-Fe), FCC (Cu, Al, Ni) and HCP ($α$-Ti, Zr) crystal lattices at T=300 K with different values of the grain-boundary phase. We derived new form of the temperature-dimensional effect. The values of extremal grain and maximum of yield strength are decreased with raising the temperature in accordance with experiments up to NC region.

cond-mat.mtrl-sci↗

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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arXiv2021

On general Lagrangian formulations for arbitrary mixed-symmetric higher-spin fermionic fields on Minkowski backgrounds

The details of unconstrained Lagrangian formulations (being continuation of earlier developed research for Bose particles in NPB 862 (2012) 270, [arXiv:1110.5044[hep-th]], Phys. of Part. and Nucl. 43 (2012) 689, [arXiv:1202.4710 [hep-th]]) are reviewed for Fermi particles propagated on an arbitrary dimensional Minkowski space-time and described by the unitary irreducible half-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 the Verma modules and finding auxiliary oscillator realizations for the orthosymplectic $osp(1|2k)$ superalgebra which encodes the second-class operator constraints subsystem in the HS symmetry superalgebra. Applying of an universal BRST-BFV approach permit to reproduce gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive fermionic fields of any spin with appropriate number of gauge and Stukelberg fields. The general construction possesses by the obvious possibility to derive Lagrangians with only holonomic constraints.

hep-th↗

arXiv2021

Statistical approach to flow stress and generalized Hall-Petch law for equilibrium polycrystalline materials

A theory of flow stress, including the yield strength is proposed for the class of PC materials with equilibrium defect structure (EDS), which is established in the PC material after series of $N_0$ similar treatments of severe plastic deformation at fixed temperature T and characterized by stabilized scalar dislocation density (SDD) and average grain size d. We calculate both the stationary SDD $ρ(b,d,T)$ and suggest a way to calculate $\varepsilon$-evolution of an equilibrium SDD $ρ_{\varepsilon}$ in PC sample under quasy-static loading depending on the average size $d$ of a grain in the range of $10^{-8}- 10^{-2}$ m, on grain boundaries orientation. The analytical dependence is realized within a disclination-dislocation mechanism in approximation of single dislocation ensemble for given phase and T. It is based on a statistical model of Boltzmann-like distribution (smoothly dependent on a strain ${\varepsilon}$) for discrete energy spectrum in each grain of a single-mode one-phase PC material with respect to quasi-stationary levels under plastic loading with the highest level equal to the energy of dislocation with maximal length. The difference of equilibrium SDD, $ρ_{\varepsilon}- ρ$, leads to a flow stress from the Taylor strain hardening mechanism containing (for $\varepsilon$ = $0.002$) the normal and anomalous Hall-Petch relations for coarse and nanocrystalline grains, respectively, and gains a maximum at floe stress values for an extreme size containing $d_0$ of order $10^{-8}- 10^{-7}$ m. The maximum undergoes a shift to the region of larger grains for decreasing temperatures, revealing temperature-dimension effect. Coincidence is well established between the theoretical and experimental data on $σ_y$ for the materials with EDS with BCC ($α$-Fe), FCC (Cu, Al, Ni) and HCP ($α$-Ti, Zr) crystal lattices with closely packed grains at T=300K.

cond-mat.mtrl-sci↗

arXiv2021

BRST-BV Quantum Actions for Constrained Totally-Symmetric Integer HS Fields

A constrained BRST-BV Lagrangian formulation for totally symmetric massless HS fields in a $d$-dimensional Minkowski space is extended to a non-minimal constrained BRST-BV Lagrangian formulation by using a non-minimal BRST operator $Q_{c|\mathrm{tot}}$ with non-minimal Hamiltonian BFV oscillators $\overline{C}, \overline{\mathcal{P}}, λ, π$, as well as antighost and Nakanishi-Lautrup tensor fields, in order to introduce an admissible self-consistent gauge condition. The gauge-fixing procedure involves an operator gauge-fixing BRST-BFV Fermion $Ψ_H$ as a kernel of the gauge-fixing BRST-BV Fermion functional $Ψ$, manifesting the concept of BFV-BV duality. A Fock-space quantum action with non-minimal BRST-extended off-shell constraints is constructed as a shift of the total generalized field-antifield vector by a variational derivative of the gauge-fixing Fermion $Ψ$ in a total BRST-BV action $S^Ψ_{0|s} = \int d η_0 \langle χ^{Ψ 0}_{\mathrm{tot}|c} \big| Q_{c|\mathrm{tot}}\big| χ^{Ψ 0}_{\mathrm{tot}|c}\rangle$. We use a gauge condition which depends on two gauge parameters, thereby extending the case of $R_ξ$-gauges. For triplet and duplet formulations we explored the representations with only traceless field-antifield and source variables. For the generating functionals of Green's functions, BRST symmetry transformations are suggested and Ward identities are obtained.

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arXiv2019

Peculiarities of temperature dependence for generalized Hall-Petch law and two-phase model for deformable polycrystalline materials

In the framework of the suggested in [arxiv:1803.08247 [cond-mat.mtrl-sci]] statistical theory of the equilibrium flow stress, including yield strength, $σ_y$, of polycrystalline materials under quasi-static (in case of tensile strain) plastic deformation in dependence on average size, d, of the crystallites (grains) in the range, $10^{-8}$ m - $10^{-2}$ m. it is found the coincidences of the theoretical and experimental data of $σ_y$ for the materials with BCC ($α$- Fe), FCC (Cu, Al, Ni) and HCP ($α$-Ti, Zr) crystal lattice at T=300K. The temperature dependence of the strength characteristics is studied. It is shown on the example of Al, that the yield strength grows with decreasing of the temperature for all grains with d greater than $3*d_0$ (with $d_0$ being extremal size of the grain for maximal $σ_y$) and then $σ_y$ decreases in the nano-crystalline region, thus determining a temperature-dimension effect. Stress-strain curves, $σ=σ(ε)$, are constructed for the pure crystalline phase of $α$-Fe with Backofen-Considére fracture criterion validity. The single-phase model of polycrystalline material is augmented by means of inclusion of a softening grain boundary phase.

cond-mat.mtrl-sci↗

arXiv2019

A quantized statistical model of flow stress and generalized Hall-Petch law for deformable polycrystalline materials. A temperature-dimension effect

A theory of flow stress (FS), reviewing and developing our research,e.g. arxiv:1803.08247;1908.09338, is proposed,including yield strength (YS) of PC materials for quasi-static plastic loading for grain of average size d in range 10^{-8}-10^{-2}m. It's based on statistical model of energy spectrum distribution in each grain of 1-mode PC sample under plastic loading,with highest level equal to maximal dislocation energy. Found distribution of scalar dislocation density leads to FS due to Taylor strain hardening containing usual and anomalous HP laws for coarse and NC grains, respectively, and reaches maximum for extreme grain size d_0 of order 10^{-8}m. Maximum undergoes shift to region of larger grains for decreasing T and increasing strains. Coincidence is established among theoretical and experimental data on YS for BCC(α-Fe), FCC(Cu,Al,Ni),HCP(α-Ti,Zr) PC materials at T=300K.The T-dependence of strength quantities is studied. It is shown using Al that YS grows with decrease in T for all grains with d>3d_0,and then YS decreases in NC region,thus determining a temperature-dimension effect (TDE).1-phase model of PC sample is extended by including softening GB phase into 2-phase model,and then by dispersion (un)hardening. A quasi-particle interpretation of crystallite energy quantization is suggested.Analytic and graphic forms of HP laws are obtained in above samples with different values of small-,large-angle GB and constant pores.The maximum of YS and respective extremal grain size of the samples are shifted by change of 2-nd phase.The T-dependence of YS in range of 150-350K for Al demonstrates the validity of TDE. An enlargement of 2-nd phase neutralizes TDE.Deformation curves for 1- and 2-mode 2-phase α-Fe PC model are constructed with Backofen-Considere fracture criterion,as compared to experimental,1-phase model data, and strongly depend on multimodality and GB

cond-mat.mtrl-sci↗

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.

hep-th↗

arXiv2019

Two-phase model of the polycrystalline aggregate with account for grain-boundary states under quasi-static deformation

The statistical theory of flow stress, including yield strength, for polycrystalline materials under quasi-static plastic deformation suggested in [arxiv:1803.08247[cond-mat.mtr-sci], arxiv:1805.08623[cond-mat.mtr-sci]] is developed in the framework of a two-phase model. Analytic and graphic forms of the generalized Hall-Petch relations are obtained for samples with BCC (α-phase Fe), FCC (Cu, Al, Ni) and HCP (α-Ti, Zr) crystalline lattices at T=300K with different values of grain-boundary (second) phase. The maximum of yield strength and respective extremal grain size of the samples are shifted by changing of the second phase. Temperature dependence in the range 100-350K for yield strength (using the example of Al) revealed its increase for closely packed nano-crystalline samples with the growth of temperature. An enlargement of the second phase in a sample neutralizes this property.

cond-mat.mes-hall↗

arXiv2019

On a joint quantized and mechanical description for the Chernov-Lüders macroband of localized deformation

We suggest a quantum procedure, based on our recent statistical theory of flow stress in polycrystalline materials under quasi-static plastic deformations, with the intention to approach a theoretical description of the Chernov-Lüders shear macroband of localized deformation, exhibited by some Fe-containing materials with a second phase beyond the yield-strength point on the stress-strain curve σ=σ(ε). The procedure makes substantial use of a quasi-particle interpretation for the minimal portion of mechanical energy in a given single-mode polycrystalline aggregate that is necessary for the thermal-fluctuation mechanism to create a 0D-defect nanopore as the initial zone of a localized deformation under external loading. Using a quasi-particle description, we obtain analytic expressions both for the scalar density of dislocations, given the size of grains, the temperature, the most probable sliding system, and for the dependence σ =σ(ε) itself. A two-level system, which characterizes the mechanism of absorption and emission of such quasi-particles (dislocons) by the crystal lattice of any grain under quasi-static loading provides an effective physical description for the emergence and propagation of the Chernov-Lüders shear macroband. An enhancement of acoustic emission observed in experiments and accompanied by the macroband phenomenon justifies the interpretation of a dislocon as a composite short-lived particle consisting of acoustic phonons. A more realistic three-level system within a two-phase model with third (with dispersion particles) phase presence for actual polycrystalline samples is also produced.

cond-mat.mes-hall↗

arXiv2019

Elements of Fedosov Geometry in Lagrangian BRST Quantization

A Lagrangian BRST quantization for generic gauge theories in general irreducible non-Abelian hypergauges is proposed on a basis of the multilevel Batalin--Tyutin formalism and a special BV--BFV dual description for a reducible gauge model in a symplectic supermanifold $\mathcal{M}_0$ locally parameterized by antifields for Lagrangian multipliers and by the fields of the BV method. The quantization rules are based on a set of nilpotent anticommuting operators $Δ^\mathcal{M}, {V}^\mathcal{M}, {U}^\mathcal{M}$ defined using some odd and even symplectic structures in a supersymplectic manifold $\mathcal{M}$ whose local representation is an odd (co)tangent bundle over $\mathcal{M}_0$ provided by the choice of a flat Fedosov connection and a compatible non-symplectic metric in $\mathcal{M}_0$. The generating functional of Green's functions is constructed in terms of general coordinates in $\mathcal{M}$ with the help of contracting homotopy operators with respect to ${V}^\mathcal{M}$ and ${U}^\mathcal{M}$. We prove the gauge independence of the S-matrix and derive the Ward identity.

hep-th↗

arXiv2018

Constrained BRST-BFV and BRST-BV Lagrangians for half-integer HS fields on $R^{1,d-1}$

Gauge invariant Lagrangian descriptions of irreducible and reducible half-integer higher-spin mixed-symmetric massless and massive representations of the Poincare group with off-shell algebraic constraints are constructed within a metric-like formulation in a $d$-dimensional flat space-time on the basis of a suggested constrained BRST approach. A Lorentz-invariant resolution of the BRST complex within the constrained BRST formulations produces a gauge-invariant Fang-Fronsdal Lagrangian entirely in terms of the initial triple gamma-traceless spin-tensor field $Ψ_{(μ)_{n}}$ with gamma-traceless gauge parameter. The triplet and quartet formulations are derived. The minimal (un)constrained BRST--BV actions for above formulations are obtained, from proposed constrained BRST--BV approach to be by appropriate tools to construct interacting constrained Lagrangians.

hep-th↗

arXiv2017

Gauge-invariant Lagrangians for mixed-antisymmetric higher spin fields

Lagrangian descriptions of irreducible and reducible integer higher-spin representations of the Poincare group subject to a Young tableaux $Y[\hat{s}_1,\hat{s}_2]$ with two columns are constructed within a metric-like formulation in a $d$-dimensional flat space-time on the basis of a BRST approach extending the results of [arXiv:1412.0200[hep-th]]. A Lorentz-invariant resolution of the BRST complex within both the constrained and unconstrained BRST formulations produces a gauge-invariant Lagrangian entirely in terms of the initial tensor field $Φ_{[μ]_{\hat{s}_1}, [μ]_{\hat{s}_2}}$ subject to $Y[\hat{s}_1,\hat{s}_2]$ with an additional tower of gauge parameters realizing the $(\hat{s}_1-1)$-th stage of reducibility with a specific dependence on the value $(\hat{s}_1-\hat{s}_2)=0,1,...,\hat{s}_1$. Minimal BRST--BV action is suggested, being proper solution to the master equation in the minimal sector and providing objects appropriate to construct interacting Lagrangian formulations with mixed-antisymmetric fields in a general framework.

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