Implementing Mach’s principle using gauge theory

Sean Gryb
Phys. Rev. D 80, 024018 – Published 16 July 2009

Abstract

We reformulate an approach fist given by Barbour and Bertotti (BB) for implementing Mach’s principle for nonrelativistic particles. This reformulation can deal with arbitrary symmetry groups and finite group elements. Applying these techniques to U(1) and SU(N) invariant scalar field theories, we show that BB’s proposal is nearly equivalent to defining a covariant derivative using a dynamical connection. We then propose a modified version of the BB method which implements Mach’s principle using gauge theory techniques and argue that this modified method is equivalent to the original. Given this connection between the particle models and Yang-Mills theories, we consider the effect of dynamic curvature as a possible generalization of the BB scheme. Since the BB method can be used as a novel way of deriving geometrodynamics, the connection with gauge theory may shed new light on the gauge properties of the gravitational field.

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  • Received 9 March 2009

DOI:https://doi.org/10.1103/PhysRevD.80.024018

©2009 American Physical Society

Authors & Affiliations

Sean Gryb

  • Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada*

  • *sgryb@perimeterinstitute.ca

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Issue

Vol. 80, Iss. 2 — 15 July 2009

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