Generalized Bundle Quantum Mechanics

TL;DR

This paper extends the fibre bundle formulation of quantum mechanics using geometric calculus to curved spacetimes, aiming for a more natural and generalized mathematical framework.

Contribution

It introduces a geometric calculus approach to quantum mechanics within fibre bundles, generalizing the formulation to curved spacetimes.

Findings

Develops a geometric calculus framework for fibre bundle quantum mechanics

Generalizes the formulation to curved spacetime scenarios

Provides mathematical tools for future research in quantum geometry

Abstract

This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of the fibre bundle in question] in a more natural way. It starts off with a review of the mathematical tools needed and then moves on to build the objects necessary.