Parasupersymmetry and N-fold Supersymmetry in Quantum Many-Body Systems I. General Formalism and second Order

Tanaka, T

Publication date

October 2006

Abstract

We propose an elegant formulation of parafermionic algebra and parasupersymmetry of arbitrary order in quantum many-body systems without recourse to any specific matrix representation of parafermionic operators and any kind of deformed algebra. Within our formulation, we show generically that every parasupersymmetric quantum system of order p consists of N-fold supersymmetric pairs with N<p or N=p and thus has weak quasi-solvability and isospectral property. We also propose a new type of non-linear supersymmetries, called quasi-parasupersymmetry, which is less restrictive than parasupersymmetry and is different from N-fold supersymmetry even in one-body systems though the conserved charges are represented by higher-order linear differential...

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Parasupersymmetry and N-fold Supersymmetry in Quantum Many-Body Systems I. General Formalism and second Order

Abstract

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Parasupersymmetry and N-fold Supersymmetry in Quantum Many-Body Systems I. General Formalism and second Order

Abstract

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