Principal Bundle
A Principal Bundle is a mathematical structure used in the field of differential geometry and topology. It consists of a base space, a total space, and a structure group. The total space is a collection of fibers, each associated with a point in the base space, where the fibers represent the different possible states or configurations of a system. The structure group acts on these fibers, providing a way to transition between different states.
In simpler terms, you can think of a principal bundle as a way to organize complex systems where each point in a space corresponds to a set of possible choices. This concept is crucial in areas like gauge theory and general relativity, where it helps describe how different physical fields interact and transform.