Heisenberg-Weyl algebra revisited: Combinatorics of words and paths

Details Heisenberg-Weyl algebra revisited: Combinatorics of words and paths Heisenberg-Weyl algebra revisited: Combinatorics of words and paths

2009-04-09

arxiv.org/abs/0904.1506v1

J. Phys. A: Math. Theor. 41, 415204 (2008)

Physics

Quantum Physics

5 pages, 3 figures

Scientific paper

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.

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