Modern Physics Letters A

ON THE STATISTICS OF SU (1, 1)q and SU (2)q COHERENT STATES

Sicong Jing, Hong-Yi Fan

Published Mar 14, 1995• 2 citations

Abstract

We find that the SU (2)q coherent state and SU (1, 1)q coherent state in the sense of statistics can be classified as q-binomial state and q-negative binomial state, respectively. Their relations with the q-Euler distribution and q-Heine distribution are discussed.

DOI: 10.1142/s0217732395000739

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Modern Physics Letters A

ON THE STATISTICS OF SU (1, 1)q and SU (2)q COHERENT STATES

Sicong Jing, Hong-Yi Fan

Published Mar 14, 1995• 2 citations

Publisher

Abstract

DOI: 10.1142/s0217732395000739

Related papers

Negative binomial and multinomial states: Probability distributions and coherent states

Hong-Chen Fu, Ryu Sasaki B

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Oct 16, 199618 citations

{)}_{\mathit{q}}

coherent state. This fact is a q extension of the fact that the ordinary binomial state is a particular su(2) coherent state when the Holstein-Primakoff transformation is employed.

su(2)

coherent states, we propose ``interpretation'' of

su(1,1)

and

su(r,1)

coherent states ``in terms of probability theory''. They will be called the ``negative binomial'' (``multinomial'') ``states'' which correspond to the ``negative'' binomial (multinomial) distribution, the non-compact counterpart of the well known binomial (multinomial) distribution. Explicit forms of the negative binomial (multinomial) states are given in terms of various boson representations which are naturally related to the probability theory interpretation. Here we show fruitful interplay of probability theory, group theory and quantum theory.