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Communications in Theoretical Physics

Normally Ordered Operator Realization of U(1/1) Supergroup and Super–Jaynes–Cummings Model

Hong-Yi Fan, Qun Lee

Published Sep 15, 1995• 5 citations
Publisher

Abstract

By making use of the technique of integration within an ordered product (IWOP) of operators and the bosonic and fermionic coherent states we derive the normally ordered operator realization of U(1/1) supergroup. Its application in calculating the superpartition function of the supersymmetric Jaynes–Cummings model is demonstrated. The antinormally ordered realization of U(1/1) is also obtained.

DOI
10.1088/0253-6102/24/2/221

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By making use of the technique of integration within an ordered product (IWOP) of operators and the bosonic and fermionic coherent states we derive the normally ordered operator realization of U(1/1) supergroup. Its application in calculating the superpartition function of the supersymmetric Jaynes–Cummings model is demonstrated. The antinormally ordered realization of U(1/1) is also obtained.
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We present a general unified approach for arranging quantum operators of optical fields into ordered products (normal ordering, antinormal ordering, Weyl ordering (or symmetric ordering)) by fashioning Dirac's symbolic method and representation theory. We propose the technique of integration within an ordered product (IWOP) of operators to realize our goal. The IWOP makes Dirac's representation theory and the symbolic method more transparent and consequently more easily understood. The beauty of Dirac's symbolic method is further revealed. Various applications of the IWOP technique, such as in developing the entangled state representation theory, nonlinear coherent state theory, Wigner function theory, etc, are presented.