用规范理论实现马赫原理
Implementing Mach's Principle Using Gauge Theory
摘要：
本文重新表述了Barthel和Bertotti（BB）提出的实现非相对论粒子马赫原理的一种方法。这种变换可以处理任意对称群和有限群元。将这些技巧应用于U（1）和SU（N）不变标量场理论，我们证明了BB的建议几乎等价于使用动力学联系定义协变导数。然后，我们提出了一个修改后的版本的BB方法实现马赫的原则，使用规范理论技术，并认为这种修改后的方法是等效的原始。考虑到粒子模型和杨-米尔斯理论之间的这种联系，我们认为动态曲率的影响是BB方案的可能推广。由于BB方法可以作为推导几何动力学的一种新方法，它与规范理论的联系可以为引力场的规范性质提供新的解释。
英文摘要：
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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