Heisenberg-Weyl algebra revisited: Combinatorics of words and paths
Quantum Physics
2009-04-10 v1
Abstract
The Heisenberg-Weyl algebra, which underlies virtually all physical representations of Quantum Theory, is considered from the combinatorial point of view. We provide a concrete model of the algebra in terms of paths on a lattice with some decomposition rules. We also discuss the rook problem on the associated Ferrers board; this is related to the calculus in the normally ordered basis. From this starting point we explore a combinatorial underpinning of the Heisenberg-Weyl algebra, which offers novel perspectives, methods and applications.
Cite
@article{arxiv.0904.1506,
title = {Heisenberg-Weyl algebra revisited: Combinatorics of words and paths},
author = {P. Blasiak and A. Horzela and G. H. E. Duchamp and K. A. Penson and A. I. Solomon},
journal= {arXiv preprint arXiv:0904.1506},
year = {2009}
}
Comments
5 pages, 3 figures