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A. Pashnev

Publications and source records attributed to A. Pashnev.

At least 19 recordsLinked to original sources
arXiv2005

BRST approach to Lagrangian construction for fermionic massless higher spin fields

We develop the BRST approach to Lagrangian formulation for all massless half-integer higher spin fields on an arbitrary dimensional flat space. General procedure of Lagrangian construction describing the dynamics of fermionic field with any spin is given. It is shown that in fermionic case the higher spin field model is a reducible gauge theory and the order of reducibility grows with the value of spin. No off-shell constraints on the fields and the gauge parameters are used. We prove that in four dimensions after partial gauge fixing the Lagrangian obtained can be transformed to Fang-Fronsdal form however, in general case, it includes the auxiliary fields and possesses the more gauge symmetries in compare with Fang-Fronsdal Lagrangian. As an example of general procedure, we derive the new Lagrangian for spin 5/2 field containing all set of auxiliary fields and gauge symmetries of free fermionic higher spin field theory.

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arXiv2004

On Higher Spin Theory: Strings, BRST, Dimensional Reductions

We briefly review some modern developments in higher spin field theory and their links with superstring theory. The analysis is based on various BRST constructions allowing to derive the Lagrangians for massive and massless higher spin fields on flat or constant curvature backgrounds of arbitrary dimensions.

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arXiv2003

On the Time Dependent Oscillator and the Nonlinear Realizations of the Virasoro Group

Using the nonlinear realizations of the Virasoro group we construct the action of the Conformal Quantum Mechanics (CQM) with additional harmonic potential. We show that $SL(2,R)$ invariance group of this action is nontrivially embedded in the reparametrization group of the time which is isomorphic to the centerless Virasoro group. We generalize the consideration to the Ermakov systems and construct the action for the time dependent oscillator. Its symmetry group is also the $SL(2,R) \sim SU(1,1)$ group embedded in the Virasoro group in a more complicated way.

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arXiv2002

The Spinning Particles as a Nonlinear Realizations of the Superworldline Reparametrization Invariance

The superdiffeomorphisms invariant description of $N$ - extended spinning particle is constructed in the framework of nonlinear realizations approach. The action is universal for all values of $N$ and describes the time evolution of $D+2$ different group elements of the superdiffeomorphisms group of the $(1,N)$ superspace. The form of this action coincides with the one-dimensional version of the gravity action, analogous to Trautman's one.

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arXiv2001

Lagrangian formulation of the massless higher integer spin fields in the AdS background

We construct the Lagrangian description of arbitrary integer higher spin massless fields on the background of the D-dimensional anti-de Sitter space. The operator constraints in auxiliary Fock space corresponding to subsidiary conditions for irreducible unitary massless representations of the D-dimensional anti-de Sitter group are formulated. Unlike flat space, the algebra of the constraints turns out to be nonlinear and analogous to the $W_3$ algebra. We construct the nilpotent BRST charge for this nonlinear algebra and derive on its basis the correct field content and gauge invariant action describing the consistent arbitrary integer spin field dynamics in $AdS$ space.

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arXiv2001

On the n=4 Supersymmetry for the FRW Model

In this work we have constructed the n=4 extended local conformal time supersymmetry for the Friedmann-Robertson-Walker (FRW) cosmological models. This is based on the superfield construction of the action, which is invariant under wordline local n=4 supersymmetry with $SU(2)_{local} \otimes SU(2)_{global}$ internal symmetry. It is shown that the supersymmetric action has the form of the localized (or superconformal) version of the action for n=4 supersymmetric quantum mechanics. This superfield procedure provides a well defined scheme for including supermatter.

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arXiv2001

Nonlinear Realizations of Superconformal Groups and Spinning Particles

The method of nonlinear realizations is applied for the conformally invariant description of the spinning particles in terms of geometrical quantities of the parameter spaces of the one dimensional N - extended superconformal groups. We develop the superspace approach to the cases of spin 0, 1/2, 1 particles and describe the alternative component approach in the application to the spin-1/2 particle.

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arXiv2001

On the mixed symmetry irreducible representations of the Poincare group in the BRST approach

The lagrangian description of irreducible massless representations of the Poincare group with the corresponding Young tableaux having two rows along with some explicit examples including the notoph and Weyl tensor is given. For this purpose is used the method of the BRST constructions adopted to the systems of second class constraints by the construction of an auxiliary representations of the algebras of constraints in terms of Verma modules.

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arXiv2000

On the Classification of N-extended Supersymmetric Quantum Mechanical Systems

In this paper some properties of the irreducible multiplets of representation for the N = (p, q) - extended supersymmetry in one dimension are discussed. Essentially two results are here presented. At first a peculiar property of the one dimension is exhibited, namely that any multiplet containing 2d (d bosonic and d fermionic) particles in M different spin states, is equivalent to a (d,d) multiplet of just 2 spin states (all bosons and all fermions being grouped in the same spin). Later, it is shown that the classification of all multiplets of this kind carrying an irreducible representation of the N - extended supersymmetry is in one-to-one correspondence with the classification of real-valued Clifford Gamma-matrices of Weyl type. In particular, p+q is mapped into D, the space-time dimensionality, while 2d is determined to be the dimensionality of the corresponding Gamma-matrices. The implications of these results to the theory of spinning particles are analyzed.

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arXiv2000

N=4 Superconformal Mechanics and the Potential Structure of AdS Spaces

The dynamics of an N=4 spinning particle in a curved background is described using the N=4 superfield formalism. The $SU(2)_{local}\times SU(2)_{global}$ N=4 superconformal symmetry of the particle action requires the background to be a real "Kähler-like" manifold whose metric is generated by a sigma-model superpotential. The anti-de-Sitter spaces are shown to belong to this class of manifolds.

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arXiv2000

Massless and spinning particles as dynamics in one dimensional (super)diffeomorphism groups

It is shown that dynamics of D+2 elements of the (super)diffeomorphism group in one (1+1 for the super) dimension describes the D - dimensional (spinning) massless relativistic particles. The coordinates of this elements (D+2 einbeins, D+2 connections and 1 additional common coordinate of higher dimensionality) play the role of coordinates, momenta and Lagrange multiplier, needed for the manifestly conformal and reparametrization invariant description of the D - dimensional (spinning) particle in terms of the D+2 - dimensional spacetime.

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arXiv2000

Partial supersymmetry breaking in Multidimensional N=4 SUSY QM

The multidimensional N=4 supersymmetric quantum mechanics (SUSY QM) is constructed and the various possibilities for partial supersymmetry breaking are discussed. It is shown that quantum mechanical models with one quarter, one half and three quarters of unbroken(broken) supersymmetries can exist in the framework of the multidimensional N=4 SUSY QM.

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arXiv2000

Auxiliary representations of Lie algebras and the BRST constructions

The method of construction of auxiliary representations for a given Lie algebra is discussed in the framework of the BRST approach. The corresponding BRST charge turns out to be non -- hermitian. This problem is solved by the introduction of the additional kernel operator in the definition of the scalar product in the Fock space. The existence of the kernel operator is proven for any Lie algebra.

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arXiv2000

On the Schrodinger Equation for the Minisuperspace Models

We obtain a time-dependent Schrodinger equation for the Friedmann - Robertson - Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necesary to include an additional action invariant under the reparametrization of time. The last one does not change the equations of motion of the system, but changes only the constraint which at the quantum level becomes time-dependent Schrodinger equation. The same procedure is applied to the supersymmetric case and the supersymmetric quantum constraints are obtained, one of them is a square root of the Schrodinger operator.

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