Graph model of the Heisenberg–Weyl algebra

Blasiak, P.; Horzela, A.; Duchamp, G. H. E.; Penson, K. A. and Solomon, A. I. (2009). Graph model of the Heisenberg–Weyl algebra. Journal of Physics: Conference Series, 213 012014.

DOI: https://doi.org/10.1088/1742-6596/213/1/012014

Abstract

We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg–Weyl algebra structure. It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple interpretation involving, for example, the natural composition of graphs. This provides a deeper insight into the algebraic structure of Quantum Theory and sheds light on the intrinsic combinatorial underpinning of its abstract formalism.

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