TL;DR
This paper reformulates the Dirac equation using Spacetime Algebra to reveal geometric structures, leading to a new gauge theory of gravity that unifies aspects of general relativity and electroweak interactions.
Contribution
It introduces a novel gauge theory gravity framework based on STA, providing new insights into unifying gravity with quantum mechanics and electroweak theory.
Findings
STA reveals geometric role of imaginary unit in Dirac equation
GTG offers a new geometric approach to GR and electroweak interactions
A variant with Majorana states incorporates zitterbewegung in electrons
Abstract
Reformulation of the Dirac equation in terms of the real Spacetime Algebra (STA) reveals hidden geometric structure, including a geometric role for the unit imaginary as generator of rotations in a spacelike plane. The STA and the real Dirac equation play essential roles in a new Gauge Theory Gravity (GTG) version of General Relativity (GR). Besides clarifying the conceptual foundations of GR and facilitating complex computations, GTG opens up new possibilities for a unified gauge theory of gravity and quantum mechanics, including spacetime geometry of electroweak interactions. The Weinberg-Salam model fits perfectly into this geometric framework, and a promising variant that replaces chiral states with Majorana states is formulated to incorporate zitterbewegung in electron states.
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