Polydimensional Supersymmetric Principles

TL;DR

This paper introduces polydimensional supersymmetric principles, extending Clifford calculus and proposing a new action principle to derive equations of motion for spinning particles in curved space, addressing longstanding theoretical questions.

Contribution

It develops a novel framework of polydimensional transformations and extends Clifford calculus, providing a new classical action principle for spinning particles in curved spacetime.

Findings

Extended Clifford calculus with independent coordinates for geometric elements

Proposed a new action principle combining distance and swept area

Derived solutions to the Papapetrou equations for spinning particles

Abstract

Systems of equations are invariant under "polydimensional transformations" which reshuffle the geometry such that what is a line or a plane is dependent upon the frame of reference. This leads us to propose an extension of Clifford calculus in which each geometric element (vector, bivector) has its own coordinate. A new classical action principle is proposed in which particles take paths which minimize the distance traveled plus area swept out by the spin. This leads to a solution of the 50 year old conundrum of `what is the correct Lagrangian' in which to derive the Papapetrou equations of motion for spinning particles in curved space (including torsion). Based on talk given at: 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa-Zihuatanejo, Mexico, June 27-July 4, 1999.