Heisenberg–Weyl algebra revisited: combinatorics of words and paths

Blasiak, P.; Duchamp, G. H. E.; Horzela, A.; Penson, K. A. and Solomon, A. (2008). Heisenberg–Weyl algebra revisited: combinatorics of words and paths. Journal of Physics A: Mathematical and General, 41 p. 415204.

DOI: https://doi.org/10.1088/1751-8113/41/41/415204

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 combinatorial underpinning of the Heisenberg–Weyl algebra, which offers novel perspectives, methods and applications.