Polydimensional Supersymmetric Principles
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.
Cite
@article{arxiv.gr-qc/9909071,
title = {Polydimensional Supersymmetric Principles},
author = {William M. Pezzaglia},
journal= {arXiv preprint arXiv:gr-qc/9909071},
year = {2007}
}
Comments
12 pages, no figures. Based on presentation available at http://www.clifford.org/wpezzag/talk/99mexico/ Submitted to International Journal of Theoretical Physics