Geodesic
Vector coherent states on Clifford algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 1, pp. 9-21

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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, octonions.
Mots-clés : quaternions 
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     author = {K. Thirulogasanthar and A. L. Hohou\'eto},
     title = {Vector coherent states on {Clifford} algebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {9--21},
     publisher = {mathdoc},
     volume = {143},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_143_1_a1/}
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K. Thirulogasanthar; A. L. Hohouéto. Vector coherent states on Clifford algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 1, pp. 9-21. http://geodesic.mathdoc.fr/item/TMF_2005_143_1_a1/