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Monogenic functions and representations of nilpotent Lie groups in quantum mechanics |
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| Authors: | Jan Cnops Vladimir V. Kisil |
| Abstract: | 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. Copyright © 1999 John Wiley & Sons, Ltd. |
| 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 |