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arXiv:hep-th/9807048 · Journal of Physics A Mathematical and General

Eigenstates of paraparticle creation operators

Sicong Jing, Charles A Nelson

Published Jan 1, 1999• 6 citations
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Abstract

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 = 2, conserved-charge parabose creation operator eigenstates are also constructed. The contour forms of the associated resolutions of unity are obtained.

DOI
10.1088/0305-4470/32/2/013

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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 = 2, conserved-charge parabose creation operator eigenstates are also constructed. The contour forms of the associated resolutions of unity are 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.
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.
It is well known that Parafermi and Parabose statistics are natural extensions of the usual Fermi and Bose ones, enhancing trilinear (anti)commutation relations instead of bilinear ones. Due to this generalization, positive parameters appear: the so-called orders of paraquantization p (= 1, 2, 3, ...) and h sub 0 (= 1/2, 1, 3/2, ...), respectively, the first value leading in each case to the usual statistics. The superpostion of the parabosonic and parafermionic operators gives rise to parasupermultiplets for which mixed trilinear relations have already been studied leading to two (nonequivalent) sets: the relative Parabose and the relative Parafermi ones. For the specific values p = 1 = 2h sub 0, these sets reduce to the well known supersymmetry. Coherent states associated with this last model have been recently put in evidence through the annihilation operator point of view and the group theoretical approach or displacement operator context. We propose to realize the corresponding studies within the new context p = 2 = 2h sub 0, being then directly extended to any order of paraquantization.