Past exam of the mathematics course of the University of Cambridge 2005 iii Paper 49 4 d Solution Created 2026-10-03 Updated 2026-10-14
The covariant Landau gauge is the zero-parameter limit of the covariant gauge family. It imposes the Lorenz gauge condition sharply. The Landau gauge photon propagator is the transverse part of the inverse from solution:Away from the pole, , matching the divergence-free condition. This is transversality to the four-momentum, rather than a projector onto only the two physical spatial photon polarizations. The Lorenz gauge equation alone still admits residual gauge transformations with ; boundary conditions and the pole prescription complete the propagator choice. The parameter limit specifies the Landau propagator without trying to invert the ungauged Maxwell operator on its longitudinal null space.