What is it about?
We generalize σ-matrices to higher arities. We build nonderived n-ary version of SU(2) using cyclic shift block matrices. The presentation of n-ary SU(2) in terms of polyadic σ-matrices is done. We generalize Pauli group in two ways by phase shifts.
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Why is it important?
The ordinary sigma matrix concept is the important tool in mathematical physics and quantum computing computations. Therefore, generalization of sigma matrices could bring new and interesing results.
Perspectives
The polyadic sigma matrices were used to construct the dynamical model having a new polyadic supersymmetry (Duplij, 2024), as the polyadic generalization of the supersymmetric quantum mechanics. In a pure mathematical viewpoint, new binary and n-ary finite groups of higher order were obtained.
Dr. Habil. (Dr. Sci. Theor. Phys.) Steven Duplij (Stepan Douplii)
University of Münster
Read the Original
This page is a summary of: Polyadic sigma matrices, Journal of Mathematical Physics, August 2024, American Institute of Physics,
DOI: 10.1063/5.0211252.
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