Monogenic Functions and Representations of Nilpotent Lie Groups in Quantum Mechanics

Details Monogenic Functions and Representations of Nilpotent Lie Groups in Quantum Mechanics Monogenic Functions and Representations of Nilpotent Lie Groups in Quantum Mechanics

1998-06-27

arxiv.org/abs/math/9806150v1

Math. Methods Appl. Sci., 22(1999), no. 4, pp. 353--373

Mathematics

Complex Variables

27 pages; LaTeX2e; no pictures

Scientific paper

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.

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