Generalized commutation relations and statistics

Robert C. Hilborn, Guglielmo Maria Tino

Irl Yale

И. В. Мингалев, О. В. Мингалев, Victor Valentinovich Vedenyapin

A. Yu. Ignatiev, V.A. Kuzmin

S. Chaturvedi, Ashok Kumar Kapoor, R. Sandhya +2 more

A generalized commutation relation of a single-mode oscillator is proposed. Bose-Einstein, Fermi-Dirac, and Greenberg's infinite statistics are shown to be special cases of this commutation relation. The Fock states, coherent states, and analogs of squeezed coherent states for this commutation relation are constructed. Finally, the quantization of a free infinite-statistics field is discussed using the Umezawa-Takahashi procedure [H. Umezawa and Y. Takahashi, Prog. Theor. Phys. 9, 14 (1953); Nucl. Phys. 51, 193 (1964)].

R. O'Raifeartaigh, Colm A. Ryan

The method of the complete set is used to study a generalized commutation relation. This commutation relation is of interest for two reasons. First, it is very similar to the commutation relations considered by various authors in connection with generalized statistics. Secondly, it allows us to investigate further a problem previously considered by Wigner, namely, Do the equations of motion determine the quantum mechanical commutation relations? '' (auth)