A Dynamical System with Q-deformed Phase Space Represented in Ordinary Variable Spaces

Details A Dynamical System with Q-deformed Phase Space Represented in Ordinary Variable Spaces A Dynamical System with Q-deformed Phase Space Represented in Ordinary Variable Spaces

2010-08-31

arxiv.org/abs/1008.5221v3

Prog.Theor.Phys.124:1019-1035,2010

Physics

Mathematical Physics

17page, 2 figures

Scientific paper

10.1143/PTP.124.1019

Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a difference operator instead of the differential operator. Then, using the path integral representation for such a dynamical system, we derive an effective short-time action, which contains interaction terms even for a free particle with q-deformed phase space. Analysis is also made on the eigenvalue problem for a particle with q-deformed phase space confined in a compact space. Under some boundary conditions of the compact space, there arises fairly different structures from $q=1$ case in the energy spectrum of the particle and in the corresponding eigenspace .

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