Abstract: The gauge field is an important research field in physics，and the fiber bundle is a hot topic inmathematics． Essentially，it is the Yang-Mills equation that connects the gauge field and the fiber bundle and be-comes theirtheoretical basis． This paper focuses on the physical concept and discusses the gauge field in physics and the fiber bundle indifferential geometry． The formation and development of related concepts，and the relation-ship with the Yang-Mills equation，so that more readers can inspire the enthusiasm of exploration and innovation in this important field，conduct in-depth research，and promote its use in physics andmathematics． Making progress in intersecting topics，especially by linking the three through the curl calculation of the vector potential，can deepen a deeper understanding of the connection of fiber bundles，because this type of problem is a newresearch direction． Among them，there are still many questions，which are worthy of in-depth exploration by thosewith lofty ideals． 

Key words:  , fiber bundles, gauge fields, quantum field theory, rotation group, symmetry, invariance ,