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A principal $G$-bundle, where $G$ denotes any topological group, is a fiber bundle $\pi :P → X$ together with a continuous right action $P × G → P$ such that $G$ preserves the fibers of $P$ and acts freely and transitively on them.

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Principal bundle approach to general relativity

You might enjoy Bleeker's book "Gauge Theory and Variational Principles" (http://www.amazon.com/Gauge-Theory-Variational-Principles-Physics/dp/0486445461). His focus is definitely more on particle the …
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