Coherent states on the circle

Details Coherent states on the circle Coherent states on the circle

2011-01-21

arxiv.org/abs/1101.4171v1

Physics

Quantum Physics

7 pages, presented at GROUP28 - "28th International Colloquium on Group Theoretical Methods in Physics", Newcastle upon Tyne,

Scientific paper

We present a possible construction of coherent states on the unit circle as configuration space. In our approach the phase space is the product Z x S^1. Because of the duality of canonical coordinates and momenta, i.e. the angular variable and the integers, this formulation can also be interpreted as coherent states over an infinite periodic chain. For the construction we use the analogy with our quantization over a finite periodic chain where the phase space was Z_M x Z_M. Properties of the coherent states constructed in this way are studied and the coherent states are shown to satisfy the resolution of unity.

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