Electromagnetism and the holomorphic properties of spacetime
- 1 September 1981
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 22 (9) , 1919-1925
- https://doi.org/10.1063/1.525165
Abstract
The Cauchy–Riemann equations of holomorphy are extended to fields in higher-dimensional spaces in a framework of Clifford algebras. The equations of holomorphy in Minkowski spacetime turn out to be the Maxwell equations in vacuum. The Lorentz gauge condition is a result of the holomorphy. Sources can be included in an extension of the residue theorem, where charges correspond to the residues.Keywords
This publication has 19 references indexed in Scilit:
- Algebras with three anticommuting elements. I. Spinors and quaternionsJournal of Mathematical Physics, 1981
- Algebras with three anticommuting elements. II. Two algebras over a singular fieldJournal of Mathematical Physics, 1981
- Realization, extension, and classification of certain physically important groups and algebrasJournal of Mathematical Physics, 1981
- Complex and quaternionic analyticity in chiral and gauge theories, IAnnals of Physics, 1980
- On regular-analytic functions with values in a Clifford algebraMathematische Annalen, 1970
- Multivector functionsJournal of Mathematical Analysis and Applications, 1968
- Multivector calculusJournal of Mathematical Analysis and Applications, 1968
- Absolute-valued algebraic algebrasBulletin of the American Mathematical Society, 1949
- Quadratic Forms Permitting CompositionAnnals of Mathematics, 1942
- ber die analytische Darstellung der regul ren Funktionen einer QuaternionenvariablenCommentarii Mathematici Helvetici, 1935