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Modern Physics Letters A

FOCK SPACE STRUCTURE FOR THE SIMPLEST PARASUPERSYMMETRIC SYSTEM

Wei-Min Yang, Sicong Jing

Published May 20, 2001• 13 citations
Publisher

Abstract

Structure of the state-vector space for a system consisting of one mode para-Bose and one mode para-Fermi degree of freedom with the same parastatistics order p is studied and a complete, orthonormal set of basis vectors in this space is constructed. There is an intrinsic double degeneracy for state vectors with m parabosons and n parafermions, where m ≠ 0, n ≠ 0 and n ≠ p. It is also shown that the degeneracy plays a key role in realization of exact supersymmetry for such a system.

DOI
10.1142/s021773230100411x

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Modern Physics Letters A•Oct 1, 1988•188 citations
Structure of the state-vector space for a system consisting of one mode para-Bose and one mode para-Fermi degree of freedom with the same parastatistics order p is studied and a complete, orthonormal set of basis vectors in this space is constructed. There is an intrinsic double degeneracy for state vectors with m parabosons and n parafermions, where m ≠ 0, n ≠ 0 and n ≠ p. It is also shown that the degeneracy plays a key role in realization of exact supersymmetry for such a system.
Structure of the state-vector space for a system consisting of one mode parabose and one mode parafermi degree of freedom with the same parastatistics order ppp is studied and a complete, orthonormal set of basis vectors in this space is constructed. There is an intrinsic double degeneracy for state vectors with mmm parabosons and nnn parafermions, where m≠0m \not= 0m=0, n≠0n \not= 0n=0, and n≠pn \not= pn=p. It is also shown that the degeneracy plays a key role in realization of exact supersymmetry for such a system.
This paper researches Fock state space structure and supersymmetry mechanics of parasystem consisting of one degree of freedom of paraboson and one degree of freedom parafermion in the case of the same order p.It is shown that except for the four extreme special states,there is an intrinsic double-degeneracy in the state space structure of a parasystem.Moreover,it is also discovered that the parasystem possesses a hidden intrinsic supersymmetry in addition to the dynamic supersymmetry,and the intrinsic supersymmetry plays a key role in the exact supersymmetry of a parasystem.
The structure of the state-vector space for the two-mode parabose system is investigated and a complete set of state-vectors is constructed. The basis vectors are orthonormal in order p=2p=2p=2. In order p=2p=2p=2, conserved-charge parabose coherent states are constructed and an explicit completeness relation is obtained.