Monogenic Functions and Representations of Nilpotent Lie Groups in Quantum Mechanics
Complex Variables
2017-11-01 v1 Mathematical Physics
Functional Analysis
math.MP
Representation Theory
Quantum Physics
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. 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.
Keywords
Cite
@article{arxiv.math/9806150,
title = {Monogenic Functions and Representations of Nilpotent Lie Groups in Quantum Mechanics},
author = {Jan Cnops and Vladimir Kisil},
journal= {arXiv preprint arXiv:math/9806150},
year = {2017}
}
Comments
27 pages; LaTeX2e; no pictures