Imaginary in all directions: an elegant formulation of special relativity and classical electrodynamics
Martin Greiter, Dirk Schuricht
TL;DR
This paper introduces a novel quaternionic and complex parameterization of space-time that simplifies Lorentz transformations and condenses Maxwell's equations into a single, elegant equation.
Contribution
It presents a new mathematical framework using complex and quaternionic units to unify Lorentz transformations and Maxwell's equations.
Findings
Lorentz transformations implemented via multiplication by complex-quaternionic numbers
Maxwell's equations reduced to a single elegant equation
Simplifies the mathematical formulation of special relativity and electrodynamics
Abstract
A suitable parameterization of space-time in terms of one complex and three quaternionic imaginary units allows Lorentz transformations to be implemented as multiplication by complex-quaternionic numbers rather than matrices. Maxwell's equations reduce to a single equation.
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