Irreducible representations of generalized oscillator operators

Jordan, T. F. ; Mukunda, N. ; Pepper, S. V. (1963) Irreducible representations of generalized oscillator operators Journal of Mathematical Physics, 4 (8). pp. 1089-1095. ISSN 0022-2488

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Official URL: http://link.aip.org/link/jmapaq/v4/i8/p1089/s1

Related URL: http://dx.doi.org/10.1063/1.1704038

Abstract

All of the irreducible representations are found for a single pair of creation and annihilation operators which together with the symmetric or antisymmetric number operator satisfy the generalized commutation relation characteristic of para-Bose or para-Fermi field quantization. The procedure is simply to identify certain combinations of these three operators with the three generators of the three-dimensional rotation group in the para-Fermi case, and with the three generators of the three-dimensional Lorentz group in the para-Bose case. The irreducible representations are then easily obtained by the usual raising and lowering operator techniques. The applicability of these techniques is demonstrated by a simple argument which shows that the commutation relations require that the generator to be diagonalized have a discrete spectrum.

Item Type:Article
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Deposited On:06 Dec 2010 13:31
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