arXiv subjects

S. A. Fedoruk

Publications and source records attributed to S. A. Fedoruk.

18 recordsLinked to original sources

arXiv2026

On BRST Lagrangian description of partially massless bosonic fields

We present an exhaustive BRST lagrangian description of partially massless bosonic fields in four-dimensional space. The basic fields are formulated in terms of two-component spin-tensors in (A)dS space where the tracelessness conditions are automatically fulfilled. The mass shell of partially massless fields is reformulated in terms of constraints on Fock space vectors including the second-class constraints. A conversion procedure for transforming second-class constraints into first-class ones is developed, allowing one to construct a Hermitian and nilpotent BRST charge in the Fock space under consideration. It is proven that the hermiticity and nilpotency restrict the conditions on the theory parameters, which are fulfilled only in dS space. The hermiticity of the BRST charge is incompatible with AdS space. The gauge invariant Lagrangian is constructed on the basis of the BRST charge, and for spin $s$ and depth $t$ the allowed states in the Lagrangian include only $(s-t-1)$ Stückelberg fields. Their exclusion leads to gauge transformations of degree $(s-t)$ for the physical fields. The Lagrangian equations of motion exactly reproduce the mass shell conditions. The Lagrangian in terms of conventional spin-tensor fields is also presented.

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arXiv2025

Continuous spin superparticle in $4D$, ${\cal N}=1$ curved superspace

We present a new particle model that describes the dynamics of a $4D,$ $\mathcal{N}{=}\,1$ continuous spin particle in $AdS_4$ superspace and is a generalization of the continuous-spin superparticle model in flat $4D$, $\mathcal{N}{=}\,1$ superspace proposed in 2506.19709 [hep-th]. The model is described by $4D$, $\mathcal{N}{=}\,1$ superspace coordinates together with commuting spinor additional variables, which are inherent ingredients of continuous spin models. The Lagrangian and the system of four bosonic and four fermionic phase space constraints are derived. The consistency condition for constraints imposes a restriction on supergeometry to be $AdS$ superpace. It is shown that the bosonic constraints are first-class constraints. A covariant procedure based on the use of additional variables is developed to divide the four fermionic constraints into first and second classes. It is proved that, unlike the flat case, only one fermionic constraint is a first-class constraint, while the other three are second-class constraints. In the flat limit, one of these second-class constraints becomes a first-class one.

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arXiv2025

Continuous spin superparticle model

We construct a new model of a particle propagating in $4D$, ${\cal N}=1$ superspace that describes the dynamics of a continuous spin irreducible representation of the Poincaré supergroup. The model is characterized by two-component Weyl spinor additional even variables playing the role of extra coordinates. A canonical formulation, specific local fermionic $κ$-symmetry, and a compete system of bosonic and fermionic constraints are derived. All bosonic constrains are first-class, while fermionic constraints are a mixture of first and second classes. Using additional variables inherent in to the model, we split the fermionic constraints into first and second classes in a covariant way. Quantization of the model is carried out according to Dirac prescription imposing all the first-class constraints and half of the second-class constraints (Gupta-Bleuler procedure) on the wave function. At quantization, the fermionic constraints are written in terms of spinor supercovariant derivatives acting on superfields. The corresponding wave function, which is either a chiral or antichiral superfield, depends on additional variables and obeys the superfield constraints that define the continuous spin irreducible representation of the Poincaré supergroup in the superspace.

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arXiv2025

On BRST Lagrangian formulation for massive higher-spin fields in $4D$ Minkowski space

We give a brief overview of the BRST approach to the gauge invariant Lagrangian formulation for free massive higher-spin bosonic fields focusing on two specific aspects. First, the theory is considered in four dimensional flat space in terms of spin-tensor fields with two component undotted and dotted indices. This leads to a significant simplification of the whole approach in comparison with the one where the fields with vector indices were used, since now there is no need to introduce a constraint responsible for the traces of the fields into the BRST charge. Second, we develop an extremely simple and clear procedure to eliminate all the auxiliary fields and prove that the BRST equations of motion identically reproduce the basic conditions for irreducible representations of the Poincáre group with a given mass and spin. Similar to the massless theory, the final Lagrangian for massive higher-spin fields is formulated in triplet form. The BRST formulation leads to a system of fields that are clearly subdivided into the basic spin $s$ field, Zinoviev-like auxiliary fields, Singh-Hagen-like auxiliary fields, and special BRST auxiliary fields. The auxiliary fields can be partially eliminated by gauge fixing and/or using the equations of motion. This allows one to obtain formally different (with different numbers of auxiliary fields) but equivalent Lagrangian formulations.

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arXiv2024

On the realization of infinite (continuous) spin field representations in AdS${}_{\mathbf{4}}$ space

We study the symmetry properties of infinite spin fields in $\rm{AdS}_4$ space which are involved in the Lagrangian model proposed in arXiv:2403.14446 where the main role is played by operator constraints. It is shown that the conditions defining infinite spin states in $\rm{AdS}_4$ space are $\mathrm{SO}(2,3)$-invariant. It is found that in the model under consideration the Casimir operators are completely fixed by the constraint operators and only one of the Casimir operators is independent. It is shown that in this model, infinite spin fields in $\rm{AdS}_4$ space are described by the most degenerate representations of the $\mathrm{SO}(2,3)$ group.

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arXiv2024

On BRST Lagrangian formulation of massless higher spin fields

The paper is dedicated to the blessed memory of Professor Vladislav Gavrilovich Bagrov, an outstanding Russian scientist in the area of theoretical and mathematical physics. He had a great influence on the formation of the scientific interests dozens of scientists in Tomsk and Russia as a whole. Two of the authors of this paper (I.L.B and V.A.K) are to one degree or another grateful to Professor V.G. Bagrov for comprehensive support in the initial period of their scientific career. Two other authors (S.A.F. and A.P.I.) are familiar with and use the work of scientists from the Tomsk School of Theoretical Physics, founded by Professor V.G. Bagrov. The paper is devoted to certain aspects of the higher-spin field theory, which were mainly initiated and continued during of I.L.B and V.A.K work in Tomsk. We demonstrate in details the simplicity and clearity of the Lagrangian formulation for free four-dimensional massless higher-spin fields within the universal BRST approach, while describing these fields in terms of two-component spin-tensors.

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arXiv2024

BRST construction for infinite spin field on $AdS_4$

We generalize the first class constraints that describe the infinite spin irreducible $4D$ Poincaré group representation in flat space to new first class constraints in $AdS_4$ space. The constraints are realized as operators acting in Fock space spanned by the creation and annihilation operators with two-component spinor indices. As a result, we obtain a new closed gauge algebra on $AdS_4$ with the known flat space limit. Using this gauge algebra, we construct the BRST charge and derive the Lagrangian and gauge transformations for free bosonic infinite spin field theory in $AdS_4$ space.

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arXiv2024

Infinite (continuous) spin particle in constant curvature space

We present a new particle model that generalize for constant curvature space an infinite spin particle in flat space. The model is described by commuting Weyl spinor additional coordinates. It proved that such a model is consistent only in external gravitational field corresponding to the constant curvature spaces. Full set of the first-class constraints in the de Sitter and anti-de Sitter spaces is obtained.

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arXiv2023

Generalization of the Bargmann-Wigner approach to constructing relativistic fields

We review the method for constructing local relativistic fields corresponding to the Bargmann-Wigner wave functions that describe the unitary irreducible representations of the $4D$ Poincaré group. The method is based on the use of the generalized Wigner operator connecting the wave functions of induced representations and local relativistic fields. Applications of this operator for constructing massive local relativistic fields as well as massless helicity local fields and massless local infinite spin fields are considered.

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arXiv2023

Lagrangian formulation for free $6D$ infinite spin field

We construct a Lagrangian that describes the dynamics of a six-dimensional free infinite (continuous) spin field in $6D$ Minkowski space. The Lagrangian is formulated in the framework of the BRST approach to higher spin field theory and is based on a system of constraints defining an irreducible representation of the corresponding Poincaré group. The field realization of generators in the $6D$ Poincaré algebra and the second-, fourth-, and sixth-order Casimir operators are obtained in explicit form using additional spinor coordinates. Specific aspects of such a realization in six dimensions are discussed. We derive the conditions that determine the irreducible representation $6D$ infinite spin field and reformulate them as operators in the Fock space forming a first-class algebra in terms of commutators. These operators are used to construct the BRST charge and the corresponding Lagrangian. We prove that the conditions of the irreducible representation are reproduced as the consequence of the Lagrangian equations of motion, which finally provides the correctness of the results obtained.

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arXiv2023

Generalized Wigner operators and relativistic gauge fields

We introduce and study the generalized Wigner operator. By definition, such an operator transforms the Wigner wave function into a local relativistic field corresponding to an irreducible representation of the Poincaré group by extended discrete transformations, with integer helicities $λ$ and $-λ$. It is shown that the relativistic fields constructed in this way are gauge potentials and satisfy the relations that determine free massless higher spin fields.

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arXiv2023

Generalization of the Bargmann-Wigner construction for infinite spin fields

We develop a generalization of the Wigner scheme for constructing the relativistic fields corresponding to irreducible representations of the four-dimensional Poincaré group with infinite spin. The fields are parameterized by a vector and an additional commuting vector or spinor variable. The equations of motion for fields of infinite spin are derived in both formulations under consideration.

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arXiv2022

Light-front description of infinite spin fields in six-dimensional Minkowski space

We present a new $6D$ infinite spin field theory in the light-front formulation. The Lorentz-covariant counterparts of these fields depend on 6-vector coordinates and additional spinor variables. Casimir operators in this realization are found. We obtain infinite-spin fields in the light-cone frame which depend on two sets of the $\mathrm{SU}(2)$-harmonic variables. The generators of the $6D$ Poincaré group and the infinite spin field action in the light-front formulation are presented.

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arXiv2022

On the off-shell superfield Lagrangian formulation of $4D$, $\mathcal{N}{=}\,1$ supersymmetric infinite spin theory

We develop a complete off-shell Lagrangian description of the free $4D, {\cal N}=1$ supersymmetric theory of infinite spin. Bosonic and fermionic fields are formulated in terms of spin-tensor fields with dotted and undotted indices. The corresponding Lagrangians for bosonic and fermionic infinite spin fields entering into the on-shell supersymmetric model are derived within the BRST method. Lagrangian for this supersymmetric model is written in terms of the complex infinite spin bosonic field and infinite spin fermionic Weyl field subject to supersymmetry transformations. The fields involved into the on-shell supersymmetric Lagrangian can be considered as components of six infinite spin chiral and antichiral multiplets. These multiplets are extended to the corresponding infinite spin chiral and antichiral superfields so that two chiral and antichiral superfields contain among the components the basic fields of an infinite spin supermultiplet and extra four chiral and antichiral superfields containing only the auxiliary fields needed for the Lagrangian formulation. The superfield Lagrangian is constructed in terms of these six chiral and antichiral supefields, and we show that the component form of this superfield Lagrangian exactly coincides with the previously found component supersymmetric Lagrangian after eliminating the component fields added to construct (anti)chiral superfields.

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arXiv2021

Twistor formulation of massless $6D$ infinite spin fields

We construct massless infinite spin irreducible representations of the six-dimensional Poincaré group in the space of fields depending on twistor variables. It is shown that the massless infinite spin representation is realized on the two-twistor fields. We present a full set of equations of motion for two-twistor fields represented by the totally symmetric $\mathrm{SU}(2)$ rank $2s$ two-twistor spin-tensor and show that they carry massless infinite spin representations. A field twistor transform is constructed and infinite spin fields are found in the space-time formulation with an additional spinor coordinate.

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arXiv2021

Massless finite and infinite spin representations of Poincaré group in six dimensions

We study the massless irreducible representations of the Poincaré group in the six-dimensional Minkowski space. The Casimir operators are constructed and their eigenvalues are found. It is shown that the finite spin (helicity) representation is defined by two integer or half-integer numbers while the infinite spin representation is defined by the real parameter $μ^2$ and one integer or half-integer number.

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arXiv2016

Bi-HKT and bi-Kaehler supersymmetric sigma models

We study CKT (or bi-HKT) N = 4 supersymmetric quantum mechanical sigma models. They are characterized by the usual and the mirror sectors displaying each HKT geometry. When the metric involves isometries, a Hamiltonian reduction is possible. The most natural such reduction with respect to a half of bosonic target space coordinates produces an N = 4 model, related to the twisted Kaehler model due to Gates, Hull and Rocek, but including certain extra F-terms in the superfield action.

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arXiv2012

Real and complex supersymmetric d=1 sigma models with torsions

We derive and discuss, at both the classical and the quantum levels, generalized N = 2 supersymmetric quantum mechanical sigma models describing the motion over an arbitrary real or an arbitrary complex manifold with extra torsions. We analyze the relevant vacuum states to make explicit the fact that their number is not affected by adding the torsion terms.

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