Implementing Mach's Principle Using Gauge Theory

Understand

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.