2022/12/12 by Erin T. Albertin, Zachary P. Bradshaw, Albertin, Erin T. +7
Mathematics · #34L40 (Secondary) #35Q41 (Primary) #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2212.06062
openalex publication_date 2022/12/12 · openalex created_date 2022/12/26 · openalex updated_date 2026/07/28
The linearization of a quadratic form gives rise to a Clifford algebra structure, as seen in Dirac's factorization of the d'Alembert operator. A similar structure known as a generalized Clifford algebra arises from the continuation of this procedure to higher order forms. This technique combined with the existence of a fractional derivative satisfying the semi-group property can be used to factor the d'Alembert operator further, producing a fractional partial differential matrix equation that has a similar form to Dirac's equation. We examine these equations, their solutions, and point out difficulties when attempting to make physical sense of them.