Physical Review A

Generalized commutation relations for a single-mode oscillator

S. Chaturvedi, Ashok Kumar Kapoor, R. Sandhya, Venkatraman Srinivasan, R. Simon

Published Apr 1, 1991• 59 citations

Abstract

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)].

DOI: 10.1103/physreva.43.4555

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Physical Review A

Generalized commutation relations for a single-mode oscillator

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Published Apr 1, 1991• 59 citations

Publisher

Abstract

DOI: 10.1103/physreva.43.4555

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\phi_{a}

and

\phi_{b}

into identity. The way of incorporating para-Grassmann numbers

\xi_{k}

into a general scheme of uniquantization is also offered. For parastatistics of order 2 a new fact is revealed, namely, the trilinear relations containing both the para-Grassmann variables

\xi_{k}

and the field operators

a_{k}

b_{m}

under a certain invertible mapping go over into the unitary equivalent relations, where commutators are replaced by anticommutators and vice versa. It is shown that the consequence of this circumstance is the existence of two alternative definitions of the coherent state for para-Fermi oscillators. The Klein transformation for Green's components of the operators

a_{k}

b_{m}

is constructed in an explicit form that enables us to reduce the initial commutation rules for the components to the normal commutation relations of ordinary Fermi fields. A nontrivial connection between trilinear commutation relations of the unitary quantization scheme and so-called Lie-supertriple system is analysed. A brief discussion of the possibility of embedding the Duffin-Kemmer-Petiau theory into the unitary quantization scheme is provided.