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arXiv · 0710.0266

Graph model of the Heisenberg-Weyl algebra

P. Blasiak·A. Horzela·G. H. E. Duchamp·K. A. Penson·A. I. Solomon
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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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P. Blasiak, A. Horzela, G. H. E. Duchamp, K. A. Penson, A. I. Solomon. 2007-10-01. Graph model of the Heisenberg-Weyl algebra. https://doi.org/10.1088/1742-6596/213/1/012014

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