Mathematical Physics

    

Non Commutative Fourier Duality on One-Dimension and Its Application

Authors: Vicente Pedro Diogo

The present article aims to present an extension of the Fourier dualityto non-commutative groups and algebraic structures,analyzing thenon-commutative Fourier transform on one dimensional structures alongwith their unitary representation. This approach gives a comprehensiveinsight into the harmonic analysis of operator-valued functions, providingmathematical foundations for analyzing physical systems that exhibitnon-commutative symmetries. Hence the article discusses applications ofnon-commutative harmonic analysis into emerging fields of physics such asquantum mechanics and models of quantum gravity , opening paths forexploration of the connections between non-commutative algebras, harmonicanalysis, and theoretical Physics.

Comments: 14 Pages.

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Submission history

[v1] 2025-08-17 22:43:19

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