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The State-Vector Space for Two-Mode Parabosons and Charged Parabose Coherent States

Jing, S, Nelson, C A

Published Jun 1, 1998• 2 citations
OpenAlex

Abstract

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 $p=2$. In order $p=2$, conserved-charge parabose coherent states are constructed and an explicit completeness relation is obtained.

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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.
Eigenstates of the parabose and parafermi creation operators are constructed. In the Dirac contour representation, the parabose eigenstates correspond to the dual vectors of the parabose coherent states. In order p=2p=2p=2, conserved-charge parabose creation operator eigenstates are also constructed. The contour forms of the associated resolutions of unity are obtained.
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.