Geodesic
Vector coherent states on Clifford algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 1, pp. 9-21 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 
@article{TMF_2005_143_1_a1,
     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},
     year = {2005},
     volume = {143},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_143_1_a1/}
}
TY  - JOUR
AU  - K. Thirulogasanthar
AU  - A. L. Hohouéto
TI  - Vector coherent states on Clifford algebras
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2005
SP  - 9
EP  - 21
VL  - 143
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2005_143_1_a1/
LA  - ru
ID  - TMF_2005_143_1_a1
ER  - 
%0 Journal Article
%A K. Thirulogasanthar
%A A. L. Hohouéto
%T Vector coherent states on Clifford algebras
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2005
%P 9-21
%V 143
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2005_143_1_a1/
%G ru
%F TMF_2005_143_1_a1
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/

[1] S. T. Ali, J.-P. Antoine, J.-P. Gazeau, Coherent States, Wavelets and their Generalizations, Springer, New York, 2000 ; J. R. Klauder, B. S. Skagerstam, Coherent States, Applications in Physics and Mathematical Physics, World Scientific, Singapore, 1985 ; А. М. Переломов, Обобщенные когерентные состояния и их применения, Наука, М., 1987 | MR | MR | Zbl | MR

[2] K. Thirulogasanthar, S. T. Ali, J. Math. Phys., 44 (2003), 5070–5083 | DOI | MR | Zbl

[3] J. R. Klauder, K. A. Penson, J.-M. Sixdeniers, Phys. Rev. A, 64 (2001), 013817 | DOI

[4] Y. Tian, Adv. Appl. Clifford Algebras, 10 (2000), 61–90 | DOI | MR | Zbl

[5] M. W. Janowicz, J. M. A. Ashbourn, Phys. Rev. A, 55 (1997), 2348–2359 | DOI

[6] P. B. Abraham, H. E. Moses, Phys. Rev. A, 22 (1980), 1333–1340 ; M. M. Nieto, Phys. Rev. D, 24 (1981), 1030–1032 | DOI | MR | DOI

[7] S. T. Ali, M. Englis, J.-P. Gazeau, J. Phys. A, 37 (2004), 6067–6089 | DOI | MR | Zbl