Aspects of Quantization: Fock Space Constructions and Deformations

Dirk Graudenz

Won Sang Chung, Mahouton Norbert Hounkonnou, Sama Arjika

In this paper, we propose a full characterization of a generalized q-deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the condition satisfied by the deformed q-number to define the algebra structure function. Particular Fock spaces involving finite and infinite dimensions are examined. A deformed calculus is performed as well as a coordinate realization for this algebra. A relevant example is exhibited. Associated coherent states are constructed. Finally, some thermodynamics aspects are computed and discussed.

F. Bayen, Mosh� Flato, Christian Frønsdal +2 more

Alexander V. Turbiner

Certain non-linear relations between the generators of the (q-deformed) Heisenberg algebra are found. Some of these relations are invariant under quantization and $q$-deformation.

Jaromir Tosiek