nLab Lorenz gauge

Idea

For electromagnetism the Lorenz gauge condition is one possible gauge fixing condition: It requests that the divergence of the gauge potential $A$ differential 1-form vanishes: $d \star A = 0$.

On Minkowski spacetime in standard coordinates this is the condition $\partial_\mu A^\mu = 0$ (using Einstein summation convention).

In BV-BRST formalism this gauge (and its variants) is implement by introducing the auxiliary “Nakanishi-Lautrup field” together with its “antighost field”, see at quantization of Yang-Mills theory.

References

Named after Ludvik Lorenz (not to be confused with Hendrik Lorentz whose name is attached to the Lorentz group).

• Marc Henneaux, section 9.1 of Lectures on the Antifield-BRST formalism for gauge theories, Nuclear Physics B (Proceedings Supplement) 18A (1990) 47-106 (pdf)