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arXiv · 2212.06062

Fractional Dirac Equations from Polynomial Linearization: Solutions and Difficulties

Erin T. Albertin·Zachary P. Bradshaw·Kaitlyn M. Kirt·Kathryn E. Long·Anthony Nguyen
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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.

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Erin T. Albertin, Zachary P. Bradshaw, Kaitlyn M. Kirt, Kathryn E. Long, Anthony Nguyen. 2022-12-12. Fractional Dirac Equations from Polynomial Linearization: Solutions and Difficulties. https://arxiv.org/abs/2212.06062

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