Quantum dynamics of massive particles in a non-commutative two-sheeted space-time

TL;DR

This paper extends the Dirac equation to a non-commutative two-sheeted space-time, predicting matter-hidden matter oscillations due to a small electromagnetic coupling, with potential observational implications.

Contribution

It introduces a novel non-commutative two-sheeted space-time framework that doubles fermionic states, linking matter and hidden matter, and predicts observable matter-hidden matter oscillations.

Findings

Prediction of matter-hidden matter oscillations.

Identification of a small electromagnetic coupling between matter and hidden matter.

Extension of Dirac theory to non-commutative two-sheeted space-time.

Abstract

We study a formal extension of the Dirac equation in the framework of a non-commutative two-sheeted space-time. It is shown that this approach naturally extends the classical Dirac theory by doubling the number of fermionic states, which can then be identified as matter and hidden-matter states. Our model exhibit several interesting features that could have observational consequences. Among them, we predict a small electromagnetic coupling between matter and hidden matter universes which should lead to matter/hidden matter oscillations in presence of intense electromagnetic vector potentials.