Monogenic Functions and Representations of Nilpotent Lie Groups in Quantum Mechanics
Cnops, Jan ; Kisil, Vladimir
arXiv, 9806150 / Harvested from arXiv
Text on arXiv
We describe several different representations of nilpotent step two Lie groups in spaces of monogenic Clifford valued functions. We are inspired by the classic representation of the Heisenberg group in the Segal-Bargmann space of holomorphic functions. Connections with quantum mechanics are described. Keywords: Segal-Bargmann space, Heisenberg group, coherent states, wavelet transform, reproducing kernel, nilpotent Lie group, monogenic functions, Dirac operator, Clifford algebra, (second) quantization, quantum field theory.
Publié le : 1998-06-27
Classification:  Mathematics - Complex Variables,  Mathematical Physics,  Mathematics - Functional Analysis,  Mathematics - Representation Theory,  Quantum Physics,  46E20,  22E27, 30G35, 30H05, 46E22, 81R05, 81R30 
@article{9806150,
     author = {Cnops, Jan and Kisil, Vladimir},
     title = {Monogenic Functions and Representations of Nilpotent Lie Groups in
  Quantum Mechanics},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9806150}
}

Cnops, Jan; Kisil, Vladimir. Monogenic Functions and Representations of Nilpotent Lie Groups in
  Quantum Mechanics. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9806150/