1998年1月
Probability distributions and coherent states of B-r, C-r, and D-r algebras
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
- ,
- 巻
- 31
- 号
- 3
- 開始ページ
- 901
- 終了ページ
- 925
- 記述言語
- 英語
- 掲載種別
- DOI
- 10.1088/0305-4470/31/3/006
- 出版者・発行元
- IOP PUBLISHING LTD
A new approach to probability theory based on quantum mechanical and Lie algebraic ideas is proposed and developed. The underlying fact is the observation that the coherent states of the Heisenberg-Weyl, su(2), su(r + 1), su(1, 1) and su(r, 1) algebras in certain symmetric (bosonic) representations give the 'probability amplitudes' (or the 'square roots') of the well known Poisson, binomial, multinomial, negative binomial and negative multinomial distributions in probability theory. New probability distributions are derived based on coherent states of the classical algebras B-r, C-r and D-r in symmetric representations. These new probability distributions are simple generalization of the multinomial distributions with some added new features reflecting the quantum and Lie algebraic construction. As byproducts, simple proofs and interpretation of addition theorems of Hermite polynomials are obtained from the 'coordinate' representation of the (negative) multinomial states. In other words, these addition theorems are higher rank counterparts of the well known generating function of Hermite polynomials, which is essentially the 'coordinate' representation of the ordinary (Heisenberg-Weyl) coherent state.
- リンク情報
- ID情報
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- DOI : 10.1088/0305-4470/31/3/006
- ISSN : 0305-4470
- CiNii Articles ID : 80010105007
- Web of Science ID : WOS:000071819200006