Infinite statistics and theSU(1, 1) phase operator

Abstract

A few years ago, Agarwal (1991 Phys. Rev. A 44 8398) showed that the Susskind–Glogower phase operators, expressible in terms of Bose operators, provide a realization of the algebra for particles obeying infinite statistics. In this paper we show that the SU(1, 1) phase operators, constructed in terms of the elements of the su(1, 1) Lie algebra, also provide a realization of the algebra for infinite statistics. There are many realizations of the su(1, 1) algebra in terms of single or multimode bose operators, three of which are discussed along with their corresponding phase states. The Susskind–Glogower phase operator is a special case of the SU(1, 1) phase operator associated with the Holstein–Primakoff realization of su(1, 1).