The Dirac Equation from the Perspective of Quaternionic Analysis

Advances in Applied Clifford Algebras 2026 Open access

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Authors: Jürgen Bolik
DOI: 10.1007/s00006-026-01436-8
Cited by: 1
References: 21

Abstract

Abstract The Dirac equation is mapped to a first order differential equation for complex quaternionic functions to benefit from potential theory and quaternionic analysis. This method provides solutions which do not depend on particular matrix representations for Clifford algebras. We additionally deduce zero-mode solutions for the Dirac–Weyl equation, when non-vanishing vector potentials are presupposed.

Fields of Study & Subjects

Algebraic and Geometric Analysis Quantum and Classical Electrodynamics Quantum Mechanics and Non-Hermitian Physics

Publication details

Journal / source
Advances in Applied Clifford Algebras
Publisher
Springer Science and Business Media LLC
Volume
36
Issue
2
Publication date
5 February 2026
Language
EN