The Mathematics of the Spinning Particle Problem

TL;DR

This paper introduces a new geometric calculus framework for analyzing functions on extended bodies, with potential applications to spinning particles in curved space, advancing the mathematical tools for physical research.

Contribution

It develops an original approach to geometric calculus for functions on extended bodies, linking it to physical models of spinning particles in curved space.

Findings

Proposed a new geometric calculus framework.

Connected the calculus to physical models of spinning particles.

Discussed the current development stage and future directions.

Abstract

We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully completed, we present it at its current stage of development, and discuss it's connection to physical research, in particular its application to spinning particles in curved space.