Gauge Symmetry in Shape Dynamics

TL;DR

This paper explores the extension of gauge symmetry concepts to shape dynamics, incorporating multiple dimensions, time dependence, and conservation laws, with potential applications in physics and deformable body dynamics.

Contribution

It generalizes the gauge symmetry framework for deformable bodies to higher dimensions and dynamic scenarios, broadening its theoretical and practical relevance.

Findings

Extended gauge symmetry to arbitrary dimensions and time dependence.

Connected gauge concepts with conservation laws in shape dynamics.

Suggested new applications in physics and material science.

Abstract

C. N. Yang's ideas about local gauge symmetry and non-integrable phases have been enormously fertile sources of inspiration in fundamental physics and in the quantum theory of matter. They also arise naturally in describing the dynamics of deformable bodies. Here I extend previous discussions of the gauge symmetry of deformable bodies in several directions, bringing in an arbitrary number of dimensions, general time-dependence, conservation laws and adiabatic residuals. I briefly indicate other potential applications of the conceptual framework.