Heisenberg–Weyl algebra revisited: Combinatorics of words and paths

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.

URI

https://doi.org/10.34657/2489
https://oa.tib.eu/renate/handle/123456789/2670

Citation

Blasiak, P., Duchamp, G. H. E., Horzela, A., Penson, K. A., & Solomon, A. I. (2009). Heisenberg–Weyl algebra revisited: Combinatorics of words and paths (Vol. 2009-02). Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach. https://doi.org//10.14760/OWP-2009-02

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Mathematik
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