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C algebra Applications in Physical System

01/24/2024 | Icon feather-clock 10 minutes

Quantum mechanics inspired a rapid development in the mathematical theories in the field of Physics.

To make the math representation theory of Quantum mechanics more formal, the great Mathematicians Dirac and von Neumann used the mathematical theory of Hilbert spaces, Operator algebra and C-Algebra, providing five axioms to summarize a common mathematical structure of quantum mechanics as developed by Heisenberg and Schrödinger. They used extensively the observables for a physical system as the set of bounded self-adjoint operators in Hilbert spaces and corresponding expectations of these observables to describe the measurement results.

Those are called the Dirac-von Neumann axioms of quantum mechanics.

The stunning thing is that C-Algebras and corresponding Hilbert spaces are NOT only used, among other mathematical fields, in Physics BUT also they can be applied in Telecom and more specifically in Wireless Communications, The use of operators to formulate the behavior of wireless transmission facilitates the processor interpretations and gives the theory a more compact and proper representation. It can be further used extensively in the forthcoming #6g networks minimizing processing load and giving a more robust description of the wireless channel.

MCNS, being always part of R&D and research projects in wireless technologies, is contributing since 2014 into this field.

This paper is the first of some contributions leading to alternative future mathematical descriptions of the physical systems and of course the Wireless Telecom world

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