Quantization and construction of second order invariants for two dimensional super systems
type: Item
instance of: scholarly article
title: Quantization and construction of second order invariants for two dimensional super systems
zbMATH Open document ID: 0723.70018
author: L. K. Tripathy
author: K. C. Tripathy
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1991-01-01T00:00:00Z
review text: The authors treat the following action in a dynamical system; \[ A=\int dt\quad L=\int dt d\theta_ i\overline{d\theta_ i}\quad {\mathfrak L}(z_ i,\quad D_ iz_ i,\quad \bar D_ iz_ i) \] with the superposition variable \(z_ i\) as a function of supertime variable, t and the Grassmann variables \(\theta_ i\) and \({\bar \theta}{}_ i\); \[ z_ i=z_ i(q_ i(t),\theta_ i,{\bar \theta}_ i)=q_ i(t)+i{\bar \theta}_ i\psi_ i(t)+i\theta_ i{\bar \psi}_ i(t)+\theta_ i{\bar \theta}_ iA_ i(t),\quad i=1,2, \] where \(\psi_ i\), \({\bar \psi}{}_ i\) and \(q_ i\), \(A_ i\) represent respectively the fermionic and bosonic spin degrees of freedom. Then by applying the Dirac's constraints the system can be reduced to a time-independent one. Thus the authors claim that the invariants in various orders of velocities and positions can be constructed. The authors construct the second order invariants involving the position, velocity and Grassmann degrees of freedom for the superharmonic oscillator and Kepler potentials.
reviewed by: Yoshihide Kozai
Mathematics Subject Classification ID: 70H99
Mathematics Subject Classification ID: 81Q60
Mathematics Subject Classification ID: 70H03
zbMATH DE Number: 4193182
zbMATH Keywords: dynamical system
zbMATH Keywords: superposition variable
zbMATH Keywords: supertime variable
zbMATH Keywords: Grassmann variables
zbMATH Keywords: Dirac's constraints
zbMATH Keywords: superharmonic oscillator
zbMATH Keywords: Kepler potentials
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4193182