arXiv subjects

A. Pichugin

Publications and source records attributed to A. Pichugin.

3 recordsLinked to original sources

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↗

arXiv1993

N=2 Super Boussinesq Hierarchy: Lax Pairs and Conservation Laws

We study the integrability properties of the one-parameter family of $N=2$ super Boussinesq equations obtained earlier by two of us (E.I. \& S.K., Phys. Lett. B 291 (1992) 63) as a hamiltonian flow on the $N=2$ super-$W_3$ algebra. We show that it admits nontrivial higher order conserved quantities and hence gives rise to integrable hierarchies only for three values of the involved parameter, $α=-2,\;-1/2,\;5/2$. We find that for the case $α= -1/2$ there exists a Lax pair formulation in terms of local $N=2$ pseudo-differential operators, while for $α= -2$ the associated equation turns out to be bi-hamiltonian.

hep-th↗

arXiv1992

Nonlinear realizations of $W_3$ symmetry

We deduce the $sl_{3}$ Toda realization of classical $W_3$ symmetry on two scalar fields in a geometric way, proceeding from a nonlinear realization of some associate higher-spin symmetry $W_{3}^{\infty}$. The Toda equations are recognized as the constraints singling out a two-dimensional fully geodesic subspace in the initial coset space of $W_{3}^{\infty}$. The proposed geometric approach can be extended to other nonlinear algebras and integrable systems.

hep-th↗