nLab gauge potential

Contents

see also at electromagnetic potential

Idea

In gauge theory in physics a field configuration is modeled, in mathematics-terminology by a connection $\nabla$ on a principal bundle $P$ (or some associated bundle). In physics-terminology the connection $\nabla$ is sometimes called the gauge potential (while the equivalence class of $P$ is called the instanton sector and the curvature $F_\nabla$ is called the field strength).

gauge field: models and components

physics	differential geometry	differential cohomology
gauge field	connection on a bundle	cocycle in differential cohomology
instanton/charge sector	principal bundle	cocycle in underlying cohomology
gauge potential	local connection differential form	local connection differential form
field strength	curvature	underlying cocycle in de Rham cohomology
gauge transformation	equivalence	coboundary
minimal coupling	covariant derivative	twisted cohomology
BRST complex	Lie algebroid of moduli stack	Lie algebroid of moduli stack
extended Lagrangian	universal Chern-Simons n-bundle	universal characteristic map

The understanding of gauge potentials as connections on fiber bundles is due to

The identification of gauge potentials with connections on fiber bundles is due to:

Tai Tsun Wu, Chen Ning Yang, Concept of nonintegrable phase factors and global formulation of gauge fields, Phys. Rev. D 12 (1975) 3845 [doi:10.1103/PhysRevD.12.3845]