Graph model of the Heisenberg-Weyl algebra
P. Blasiak, A. Horzela, G.H.E. Duchamp, K.A. Penson, A.I. Solomon
TL;DR
This paper develops a combinatorial graph-based model of the Heisenberg-Weyl algebra to provide deeper algebraic insights into Quantum Theory's formalism.
Contribution
It introduces a graph operator calculus that interprets the algebraic structure of Quantum Theory through graph composition, offering new combinatorial perspectives.
Findings
Graph operator calculus simplifies the interpretation of the Heisenberg-Weyl algebra.
The model reveals the combinatorial foundations underlying quantum algebraic structures.
The approach enhances understanding of quantum formalism through graph-based methods.
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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