Vector coherent states on Clifford algebras. (English) Zbl 1178.81118
Theor. Math. Phys. 143, No. 1, 494-504 (2005); translation from Teor. Mat. Fiz. 143, No. 1, 494-504 (2005).
Summary: 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.
MSC:
| 81R30 | Coherent states |
| 81S05 | Commutation relations and statistics as related to quantum mechanics (general) |
| 47N50 | Applications of operator theory in the physical sciences |
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