Phase operator problem and an index theorem for Q-deformed oscillator

Details Phase operator problem and an index theorem for Q-deformed oscillator Phase operator problem and an index theorem for Q-deformed oscillator

1996-03-19

arxiv.org/abs/hep-th/9603130v2

Physics

High Energy Physics

High Energy Physics - Theory

13 pages. A misprint in eq.(40) in the original version was corrected

Scientific paper

The notion of index is applied to analyze the phase operator problem associated with the photon. We clarify the absence of the hermitian phase operator on the basis of an index consideration. We point out an interesting analogy between the phase operator problem and the chiral anomaly in gauge theory, and an appearance of a new class of quantum anomaly is noted. The notion of index, which is invariant under a wide class of continuous deformation, is also shown to be useful to characterize the representations of Q-deformed oscillator algebra.

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