arXiv subjects

A. A. Deriglazov

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

52 records · Page 3Linked to original sources

arXiv1999

Green-Schwarz type formulation of D=11 S - invariant superstring and superparticle actions

A manifestly Poincare invariant formulations for $SO(1,10)$ and SO(2,9) superstring actions are proposed. The actions are invariant under a local fermionic $κ$-symmetry as well as under a number of global symmetries, which turn out to be on-shell realization of the known ``new supersymmetry`` S-algebra. Canonical quantization of the theory is performed and relation of the quantum state spectrum with that of type IIA Green-Schwarz superstring is discussed. Besides, a mechanical model is constructed, which is a zero tension limit of the D=11 superstring and which incorporates all essential features of the latter. A corresponding action invariant under off-shell closed realization of the S-algebra is obtained.

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arXiv1998

Classical description of spinning degrees of freedom of relativistic particles by means of commuting spinors

We consider a possibility to describe spin one-half and higher spins of massive relativistic particles by means of commuting spinors. We present two classical gauge models with the variables $x^μ,ξ_α,χ_α$, where $ξ,χ$ are commuting Majorana spinors. In course of quantization both models reproduce Dirac equation. We analyze the possibility to introduce an interaction with an external electromagnetic background into the models and to generalize them to higher spin description. The first model admits a minimal interaction with the external electromagnetic field, but leads to reducible representations of the Poincare group being generalized for higher spins. The second model turns out to be appropriate for description of the massive higher spins. However, it seams to be difficult to introduce a minimal interaction with an external electromagnetic field into this model. We compare our approach with one, which uses Grassman variables, and establish a relation between them.

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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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arXiv1998

Examples of D=11 S-supersymmetric actions for point-like dynamical systems

A non standard super extensions of the Poincare algebra (S-algebra [1,2]), which seems to be relevant for construction of various D=11 models, are studied. We present two examples of actions for point-like dynamical systems, which are invariant under off-shell closed realization of the S-algebra as well as under local fermionic $κ$-symmetry. On this ground, an explicit form of the S-algebra is advocated.

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arXiv1998

On zero modes of the eleven dimensional superstring

It is shown that recently pointed out by Berkovits on-shell degrees of freedom of the D=11 superstring do not make contributions into the quantum states spectrum of the theory. As a consequence, the spectrum coincides with that of the D=10 type IIA superstring.

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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

Eleven Dimensional Superstring with New Supersymmetry and D=10 type 2A Green-Schwarz Superstring

A covariant action for closed D=11 superstring with local $κ$-symmetry and global supersymmetry transformations obeying the algebra $\{Q_α,Q_β\}=CΓ^{μν}P_μn_ν$ is suggested. Physical sector variables of the model and their dynamics exactly coincide with those of the D=10 type IIA Green-Schwarz superstring. It is shown that action of the D=10 type IIA Green-Schwarz superstring can be considered as a partially gauge fixed version of the D=11 superstring action.

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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

BFV-Type Representation of Path-Integral for Dynamical System with second class constraints

It is shown that the phase space of a dynamical system subject to second class constraints can be extended by ghost variables in such a way that some formal analogies of the $Ω$-charge and the unitarizing Hamiltonian can be constructed. Then BFV-type path integral representation for the generating functional of Green's functions is written and shown to coincide with the standard one.

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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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arXiv1995

Notes on Lagrangean and Hamiltonian Symmetries

The Hamiltonization of local symmetries of the form $δq^A = \ea{R_a}^A(q,\dot q)$ or $δq^A = \dot\ea{R_a}^A (q,\dot q)$ for arbitrary Lagrangean model $L(q^A,\dot q^A)$ is considered. We show as the initial symmetries are transformed in the transition from $L$ to first order action, and then to the Hamiltonian action $S_H=\int{\rm d}τ(p_A\dot q^A-H_0-v^αΦ_α)$, where $Φ_α$ are the all (first and second class) primary constraints. An exact formulae for local symmetries of $S_H$ in terms of the initial generators ${R_a}^A$ and all primary constraints $Φ_α$ are obtained.

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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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