q-deformed oscillator algebra and an index theorem for the photon phase operator
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 correspo...
| Main Authors: | , , |
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| Language: | English |
| Published: |
1995
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| Subjects: | |
| Online Access: | http://cds.cern.ch/record/280946 |
| Summary: | 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. |
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