Heisenberg-Weyl algebra revisited: Combinatorics of words and paths

Blasiak, P.; Horzela, A.; Duchamp, G. H. E.; Penson, K. A.; Solomon, A. I.

Heisenberg-Weyl algebra revisited: Combinatorics of words and paths

Authors

Description

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.
5 pages, 3 figures