This article is cited in 1 paper

Vector coherent states on Clifford algebras

K. Thirulogasanthar, A. L. Hohouéto

Concordia University, Department of Mathematics and Statistics

Abstract: The well-known canonical coherent states are expressed as infinite series in powers of a complex number $z$ and a positive integer $\rho(m)=m!$. In analogy with the canonical coherent states, we present a class of vector coherent states by replacing the complex variable $z$ with a real Clifford matrix. We also present another class of vector coherent states by simultaneously replacing $z$ with a real Clifford matrix and $\rho(m)$ with a real matrix. As examples, we present vector coherent states labeled by quaternions and octonions with their real matrix representations. We also present a physical example.

Keywords: vector coherent states, Clifford algebras, quaternions, octonions.

Received: 28.11.2003
Revised: 29.03.2004

DOI: 10.4213/tmf1800

 English version: Theoretical and Mathematical Physics, 2005, 143:1, 494–504

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