Vector coherent states on Clifford algebras

Abstract

The well-known canonical coherent states are expressed as infinite series in powers of a complex number z and a positive integer ρ(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 ρ(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.