Year: 2022
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Albertin, Erin T., Bradshaw, Zachary P., Kirt, Kaitlyn M., Long, Kathryn E., Nguyen, Anthony
Institutions: Tulane University, Louisiana State University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4311432124