nLab gauge field - table

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