nLab higher gauge transformation




physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

Differential cohomology

Equality and Equivalence



In gauge theory two configurations ϕ 1,ϕ 2\phi_1, \phi_2 of gauge fields may be different and still be equivalent: there may be a gauge transformation λ:ϕ 1ϕ 2\lambda \colon \phi_1 \to \phi_2 between them.

In higher gauge theory also gauge transformations themseves may be different but still equivalent: if there is a gauge-of-gauge transformation ρ:λ 1λ 2\rho \colon \lambda_1 \to \lambda_2 between them.

These higher order gauge transformations are maybe best known in the physics literature in terms of their infinitesimal approximation, the BRST complex: here the gauge transformations correspond to ghost fields and the gauge-of-gauge transformations to ghost-of-ghost fields.


A basic example of a gauge field that has higher order gauge transformations is the B-field. But also magnetic current, if described properly, exhibits higher gauge transformations, see at Dirac charge quantization.

For more see at geometry of physics.


Survey of higher gauge theory:

Last revised on January 4, 2024 at 12:40:05. See the history of this page for a list of all contributions to it.