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A. Pashnev

Publications and source records attributed to A. Pashnev.

31 records · Page 2Linked to original sources
arXiv1999

Reparametrization Invariance and the Schrödinger Equation

In the present work we consider a time-dependent Schrödinger equation for systems invariant under the reparametrization of time. We develop the two-stage procedure of construction such systems from a given initial ones, which is not invariant under the time reparametrization. One of the first-class constraints of the systems in such description becomes the time-dependent Schrödinger equation. The procedure is applicable in the supersymmetric theories as well. The $n=2$ supersymmetric quantum mechanics is coupled to world-line supergravity, and the local supersymmetric action is constructed leading to the square root representation of the time-dependent Schrödinger equation.

hep-th↗
arXiv1999

N=4 Supersymmetric Multidimensional Quantum Mechanics, Partial SUSY Breaking and Superconformal Quantum Mechanics

The multidimensional N=4 supersymmetric quantum mechanics (SUSY QM) is constructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the considered SUSY QM both classical and quantum N=4 algebras include central charges, and this opens various possibilities for partial supersymmetry breaking. 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, while the one-dimensional N=4 SUSY QM, constructed earlier, admits only one half or total supersymmetry breakdown. We illustrate the constructed general formalism, as well as all possible cases of the partial SUSY breaking taking as an example a direct multidimensional generalization of the one-dimensional N=4 superconformal quantum mechanical model. Some open questions and possible applications of the constructed multidimensional N=4 SUSY QM to the known exactly integrable systems and problems of quantum cosmology are briefly discussed.

hep-th↗
arXiv1998

On a different BRST constructions for a given Lie algebra

The method of the BRST quantization is considered for the system of constraints, which form a Lie algebra. When some of the Cartan generators do not imply any conditions on the physical states, the system contains the first and the second class constraints. After the introduction auxiliary bosonic degrees of freedom for these cases, the corresponding BRST charges with the nontrivial structure of nonlinear terms in ghosts are constructed.

hep-th↗
arXiv1998

Description of the higher massless irreducible integer spins in the BRST approach

The BRST approach is applied to the description of irreducible massless higher spins representations of the Poincare group in arbitrary dimensions. The total system of constraints in such theory includes both the first and the second class constraints. The corresponding nilpotent BRST charge contains terms up to the seventh degree in ghosts.

hep-th↗
arXiv1998

Lax pairs for N=2,3 Supersymmetric KdV Equations and their Extensions

We present the Lax operator for the N=3 KdV hierarchy and consider its extensions. We also construct a new infinite family of N=2 supersymmetric hierarchies by exhibiting the corresponding super Lax operators. The new realization of N=4 supersymmetry on the two general N=2 superfields, bosonic spin 1 and fermionic spin 1/2, is discussed.

solv-int↗
arXiv1997

Nonlinear realizations of superconformal and W algebras as embeddings of strings

We propose a simple method for constructing representations of (super)conformal and nonlinear W-type algebras in terms of their subalgebras and corresponding Nambu-Goldstone fields. We apply it to N=2 and N=1 superconformal algebras and describe in this way various embeddings of strings and superstrings for which these algebras and their subalgebras define world-sheet symmetries. Besides reproducing the known examples, we present some new ones, in particular an embedding of the bosonic string with additional U(1) affine symmetry into N=2 superstring. We also apply our method to the nonlinear $W_3^{(2)}$ algebra and demonstrate that the linearization procedure worked out for it some time ago gets a natural interpretation as a kind of string embedding. All these embeddings include the critical ones as particular cases.

hep-th↗
arXiv1996

On the BRST approach to the description of a Regge trajectory

The free field theory for Regge trajectory is described in the framework of the BRST - quantization method. The physical spectrum includes daugther trajectories along with parent one. The applicability of the BRST approach to the description of a single Regge trajectory without its daughter trajectories is discussed. The simple example illustrates the appropriately modified BRST construction for the needed second class constraints.

hep-th↗
arXiv1996

The canonical quantization of the kink -- model beyond the static solution

A new approach to the quantization of the relativistic kink - model around the solitonic solution is developed on the ground of the collective coordinates method. The corresponding effective action is proved to be the action of the nonminimal $d=1+1$ point - particle with curvature. It is shown that upon canonical quantization this action yields the spectrum of kink - solution obtained firstly with the help of the WKB - quantization.

hep-th↗
arXiv1995

On the Structure of the $N=4$ Supersymmetric Quantum Mechanics in $D=2$ and $D=3$

The superfield formulation of two - dimensional $N=4$ Extended Supersymmetric Quantum Mechanics (SQM) is described. It is shown that corresponding classical Lagrangian describes the motion in the conformally flat metric with additional potential term. The Bose and Fermi sectors of two- and three-dimensional $N=4$ SQM are analyzed. The structure of the quantum Hamiltonians is such, that the usual Shrödinger equation in the flat space arises after some unitary transformation, demonstrating the effect of transmutation of the coupling constant and the energy of the initial model in some special cases.

hep-th↗
arXiv1994

Nonlinear Realizations of the $W_3^{(2)}$ Algebra

In this letter we consider the nonlinear realizations of the classical Polyakov's algebra $W_3^{(2)}$. The coset space method and the covariant reduction procedure allow us to deduce the Boussinesq equation with interchanged space and evolution coordinates. By adding one more space coordinate and introducing two copies of the $W_3^{(2)}$ algebra, the same method yields the $sl(3,R)$ Toda lattice equations.

hep-th↗
arXiv1992

Twistor-Like Type II Superstring and Bosonic String

The superfield formulation of type II Green-Schwarz superstring with n= (1,0) worldsheet supersymmetry is constructed. It is shown that the inclusion of the second spinor coordinate in the target superspase leads to the possibility of the reparametrization invariant description of the superstring in the absence of any field from the two dimensional supergravity multiplet. The twistor-like action of Chern-Simons type for bosonic string in D=3,4,6,10 is obtained from the component form of the superstring action.

hep-th↗