Particle-antiparticle duality from an extra time-like dimension

TL;DR

This paper explores how adding an extra time-like dimension to Minkowski spacetime's Clifford algebra offers new insights into particle-antiparticle duality, eigenstates, and effective scales without compactification.

Contribution

It introduces a novel interpretation of Dirac particles and antiparticles as eigenstates of rotation generators in an extended spacetime with an extra time-like dimension.

Findings

Eigenstates of rotation generator correspond to particles and antiparticles.

An effective finite scale for the extra dimension is identified without compactification.

A gauge condition preserves the scale in the presence of electromagnetic fields.

Abstract

It is a well known fact that the usual complex structure on the real Clifford Algebra (CA) of Minkowski spacetime can be obtained by adding an extra time-like dimension, instead of the usual complexification of the algebra. In this article we explore the consequences of this approach and reinterpret known results in this new context. We observe that Dirac particles and antiparticles at rest can be interpreted as eigenstates of the generator of rotations in the plane formed by the two time-like coordinates and find an effective finite scale for the extra dimension when no EM fields are present (without postulating compactness). In the case of non-vanishing EM fields, we find a gauge condition to preserve such a scale.