q-deformed oscillator algebra and an index theorem for the photon phase operator

• Main Authors: Fujikawa, K, Kwek, L C, Oh, C H
• Language: English
• Published: 1995
• Subjects: Particle Physics - Theory; DML
• Online Access: http://cds.cern.ch/record/280946

The quantum deformation of the oscillator algebra is studied from the view point of an index theorem. It is shown that the creation and annihilation operators satisfying \dml a - \dml a^{\dagger} = 1 can be deformed to \dml a - \dml a^{\dagger} = 0 in a singular limit \dml a = \infty, which corresponds to the deformation parameter q as a primitive root of unity. On the other hand, the phase operator of Susskind and Glogower, which satisfies \dml \expon^{i \varphi} - \dml (\expon^{i \varphi})^{\dagger} = 1, cannot be deformed to a hermitian phase operator which satisfies \dml \expon^{i \phi} - \dml (\expon^{i \phi})^{\dagger} = 0. The indices associated with phase operators are quite robust and may be regarded as responsible for the absence of the hermitian phase operator of the photon.