Gauge-invariant quantization for open electromagnetism

Develop a consistent, gauge-invariant quantization prescription for the dissipative Abelian gauge theory of open electromagnetism constructed in the Schwinger–Keldysh formalism, resolving the ghost-like mode encountered in covariant gauges and ensuring gauge-invariant physical observables, potentially by adapting BRST and Faddeev–Popov techniques.

Background

Within open electromagnetism, the eigenvalue structure includes a mode that would be problematic upon quantization in covariant gauges, analogous to the negative-norm Lorentz-gauge ghost in ordinary Maxwell theory. The paper emphasizes that, although classical gauge-invariant results are obtained, a fully consistent quantum prescription in the open (dissipative) setting has not been established.

The authors point to BRST and Faddeev–Popov methods as likely ingredients for such a construction, but leave the explicit development open.