Heisenberg-Weyl algebra revisited: combinatorics of words and paths
MFO Scientific ProgramOWLF 2008
Duchamp, Gérard H. E.
Penson, Karol A.
Solomon, Allan I.
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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.