arXiv subjects

M. A. Podoinitsyn

Publications and source records attributed to M. A. Podoinitsyn.

7 recordsLinked to original sources

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.

hep-th↗

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.

hep-th↗

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.

hep-th↗

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.

hep-th↗

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.

hep-th↗

arXiv2020

D-dimensional spin projection operators for arbitrary type of symmetry via Brauer algebra idempotents

A new class of representations of the Brauer algebra that centralizes the action of orthogonal and symplectic groups in tensor spaces is found. These representations make it possible to apply the technique of building primitive orthogonal idempotents of the Brauer algebra to the construction of integer spin Behrends-Fronsdal type projectors of an arbitrary type of symmetries.

hep-th↗

arXiv2017

Two-spinor description of massive particles and relativistic spin projection operators

On the basis of the Wigner unitary representations of the covering group ISL(2,C) of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the Dirac-Pauli-Fierz equations. In the framework of the two-spinor formalism we construct spin-vectors of polarizations and obtain conditions that fix the corresponding relativistic spin projection operators (Behrends-Fronsdal projection operators). With the help of these conditions we find explicit expressions for relativistic spin projection operators for integer spins (Behrends-Fronsdal projection operators) and then find relativistic spin projection operators for half integer spins. These projection operators determine the nominators in the propagators of fields of relativistic particles. We deduce generalizations of the Behrends-Fronsdal projection operators for arbitrary space-time dimensions D>2.

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