Special relativity in complex vector algebra
Garret Sobczyk
TL;DR
This paper explores the formulation of special relativity within a complex 4-dimensional algebraic framework, providing an alternative mathematical language to Minkowski space-time algebra.
Contribution
It introduces a complex 4D algebra of observables that is algebraically isomorphic to Hestenes' space-time algebra, offering a new perspective for describing special relativity.
Findings
Demonstrates the algebraic isomorphism between the complex algebra and Hestenes' algebra
Provides a new mathematical language for special relativity
Enhances understanding of algebraic structures in relativistic physics
Abstract
Many different mathematical languages have been invented to describe the ideas of Einstein's special relativity. One of the most powerful languages is the Minkowski space-time algebra of D. Hestenes. We discuss the ideas of special relativity in a complex 4-dimensional algebra of observables, which is algebraically isomorphic to the even subalgebra of Hestenes' space-time algebra.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology