Gauge Theories and Fiber Bundles: Definitions, Pictures, and Results

Understand

A pedagogical but concise overview of fiber bundles and their connections is provided, in the context of gauge theories in physics.

• The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems.
• Special attention is given to detailed figures and geometric viewpoints, some of which would seem to be novel to the literature.
• Topics are avoided which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations.