Quantum Dynamics in Regions of Quaternionic Curvature

TL;DR

This paper explores how extending quantum mechanics to quaternionic spacetime affects particle dynamics, introducing new interactions and potential dissipative effects, with an analysis of an interferometric experiment demonstrating these phenomena.

Contribution

It introduces a quaternionic generalization of quantum mechanics and analyzes its implications for particle dynamics and potential experimental detection.

Findings

Quaternionic structure influences quantum particle behavior.

Hyper-complex wavefunction components interact via potentials.

Interferometric experiments can reveal quaternionic effects.

Abstract

The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by inhomogeneous Dirac and Schr\"{o}dinger equations. Mixing of hyper-complex components of wavefunctions occurs through their interaction with potentials dissipative into the extra quaternionic degrees of freedom. An interferometric experiment is analysed to illustrate the effect.