Deformed boson algebra and projection operator of vacuum in noncommutative phase space. (English) Zbl 1170.81391
Summary: In this paper we introduce a new formalism to analyze Fock space structure of noncommutative phase space (NCPS). Based on this new formalism, we derive deformed boson commutation relations and study corresponding deformed Fock space, especially its vacuum structure, which leads to get a form of the vacuum projection operator. As an example of applications of such an operator, we define two-mode coherent state in the NCPS and show its completeness relation.
MSC:
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 81S05 | Commutation relations and statistics as related to quantum mechanics (general) |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
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