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A. V. Galajinsky

Publications and source records attributed to A. V. Galajinsky.

15 recordsLinked to original sources
arXiv2008

Quartet unconstrained formulation for massive higher spin fields

We generalize the unconstrained description of free massless higher spin fields previously developed in [Nucl.Phys. B 779 (2007) 155] to the case of free massive higher spin fields in a flat space of arbitrary dimension. The Lagrangian is given in an easy-to-handle form for an arbitrary value of spin. It is local, free from higher derivative terms, and involves a minimal number of auxiliary fields needed for an unconstrained gauge invariant description of a free massive higher spin field in arbitrary dimension.

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arXiv2008

Remark on quantum mechanics with conformal Galilean symmetry

Conformal Galilei algebra contains so(1,2) subalgebra which is the conformal algebra in one dimension. In this note we generalize methods previously developed for one-dimensional many-body systems and construct a unitary map relating a quantum mechanics invariant under the conformal Galilean transformations to a set of decoupled particles for which the same symmetry is realized in a nonlocal way. Possible applications of the map are discussed.

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arXiv2007

Quartet unconstrained formulation for massless higher spin fields

We construct simple unconstrained Lagrangian formulations for massless higher spin fields in flat space of arbitrary dimension and on anti de Sitter background. Starting from the triplet equations of Francia and Sagnotti, which describe a chain of spin modes, we introduce an auxiliary field and find appropriate gauge invariant constraints that single out the spin-s mode. The resulting quartet of fields, thus describing an irreducible representation of the Poincare group, is used to construct simple Lagrangian formulations, which are local, free from higher derivative terms and use equal number of auxiliary fields for an unconstrained description of any value of spin. Our method proves to be most efficient for an unconstrained description of massless higher spin fermions in anti de Sitter space. A relation of the minimal models with the universal BRST approach is discussed.

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arXiv2004

New insight into WDVV equation

We show that Witten-Dijkgraaf-Verlinde-Verlinde equation underlies the construction of N=4 superconformal multi--particle mechanics in one dimension, including a N=4 superconformal Calogero model.

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arXiv2004

Making the hyper--Kähler structure of N=2 quantum string manifest

We show that the Lorentz covariant formulation of N=2 string in a curved space reveals an explicit hyper--Kähler structure. Apart from the metric, the superconformal currents couple to a background two--form. By superconformal symmetry the latter is constrained to be holomorphic and covariantly constant and allows one to construct three complex structures obeying a (pseudo)quaternion algebra.

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arXiv1998

On possible generalization of the superstring action to eleven dimensions

We suggest a D=11 super Poincaré invariant action for the superstring which has free dynamics in the physical variables sector. Instead of the standard approach based on the searching for an action with local $κ$-symmetry (or, equivalently, with corresponding first class constraints), we propose a theory with fermionic constraints of second class only. Then the $κ$-symmetry and the well known $Γ$-matrix identities are not necessary for the construction. Thus, at the classical level, the superstring action of the type described can exist in any spacetime dimensions and the known brane-scan can be revisited.

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arXiv1997

A Covariant Action for the Eleven Dimensional Superstring

We suggest a super Poincaré invariant action for closed eleven dimensional superstring. The sector of physical variables $x^i$, $θ_a$, $\barθ_{\dot a}$, with $a,\dot a=1...8$ and $x^i$ the transverse part of the D=11 $x^μ$ coordinate is shown to possess free dynamics.

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arXiv1997

Massless Wess-Zumino model as first quantized Siegel superparticle

It is shown that canonical quantization of the $4d$ Siegel superparticle yields massless Wess-Zumino model as an effective field theory. Quantum states of the superparticle are realized in terms of the real scalar superfields which prove to be decomposed into the sum of on-shell chiral and antichiral superfields.

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arXiv1997

A linear realization for the new space-time superalgebras in ten and eleven dimensions

The new extensions of the Poincaré superalgebra recently found in ten and eleven dimensions are shown to admit a linear realization. The generators of the nonlinear and linear group transformations are shown to fall into equivalent representations of the superalgebra. The parametrization of the coset space $G/H$, with $G$ a given extended supergroup and $H$ the Lorentz subgroup, that corresponds to the linear transformations is presented.

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arXiv1996

Covariant Supplementation Scheme for Infinitely Reducible First Class Constraints

For a rather broad class of dynamical systems subject to mixed fermionic first and second class constraints or infinitely reducible first class constraints (IR1C), a manifestly covariant scheme of supplementation of IR1C to irreducible ones is proposed. For a model with IR1C only, an application of the scheme leads to a system with covariantly splitted and irreducible first and second class constraints. Modified Lagrangian formulations for the Green--Schwarz superstring, Casalbuoni--Brink--Schwarz superparticle and Siegel superparticle, which reproduce the supplementation scheme, are suggested.

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arXiv1996

The Green--Schwarz Superstring in Extended Configuration Space and Infinitely Reducible First Class Constraints Problem

The Green--Schwarz superstring action is modified to include some set of additional (on-shell trivial) variables. A complete constraints system of the theory turns out to be reducible both in the original and in additional variable sectors. The initial $8s$ first class constraints and $8c$ second class ones are shown to be unified with $8c$ first and $8s$ second class constraints from the additional variables sector, resulting with $SO(1,9)$-covariant and linearly independent constraint sets. Residual reducibility proves to fall on second class constraints only.

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arXiv1995

Weak Dirac bracket construction and the superparticle covariant quantization problem

The general procedure of constructing a consistent covariant Dirac-type bracket for models with mixed first and second class constraints is presented. The proposed scheme essentially relies upon explicit separation of the initial constraints into infinitely reducible first and second class ones (by making use of some appropriately constructed covariant projectors). Reducibility of the second class constraints involved manifests itself in weakening some properties of the bracket as compared to the standard Dirac one. In particular, a commutation of any quantity with the second class constraints and the Jacobi identity take place on the second class constraints surface only. The developed procedure is realized for N=1 Brink--Schwarz superparticle in arbitrary dimension and for N=1, D=9 massive superparticle with Wess--Zumino term. A possibility to apply the bracket for quantizing the superparticles within the framework of the recent unified algebra approach by Batalin and Tyutin [20--22] is examined. In particular, it is shown that for D=9 massive superparticle it is impossible to construct Dirac-type bracket possessing (strong) Jacobi identity in a full phase space.

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arXiv1994

(1,0) superparticle in a curved background and the full set of (1,0) supergravity constraints

The classical (1,0) superparticle in a curved superspace is considered. The minimal set of constraints to be imposed on the background for correct inclusion of interaction is found. The most general form of Siegel-type local fermionic symmetry is presented. Local algebra of the theory is shown to be closed off-shell and nontrivially deformed as compared to the flat one. The requirements leading to the full set of (1,0) supergravity constraints are presented.

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arXiv1994

Geometrical formulation for the Siegel superparticle}

In the superspace $z^M = (x^μ,θ_R,θ_L)$ the global symmetries for $d$ = 10 superparticle model with kinetic terms both for Bose and Fermi variables are shown to form a superalgebra, which includes the Poincaré superalgebra as a subalgebra. The subalgebra is realized in the space of variables of the theory by a nonstandard way. The local version of this model with off-shell closed Lagrangian algebra of gauge symmetries and off-shell global supersymmetry is presented. It is shown that the resulting model is dynamically equivalent to the Siegel superparticle.

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