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In the Lorenz gauge in electrodynamics, the timelike and longitudinal components can be eliminated by prescribing the Gupta-Bleuler condition $\partial^{\mu}A_{\mu}|\Psi)$ on physical states. This gives a condition $\square\Lambda=0$ on gauge transformations. In a similar fashion, is it possible to derive the Faddeev-Popov ghosts and the ghost Lagrangian in the canonical formalism in such a way that Lorentz invariance is maintained?

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Comments to the post (v2):

  1. The traditional canonical/Hamiltonian formalism breaks manifest Lorentz covariance (but is still implicitly Lorentz covariant as it must agree with the covariant/Lagrangian formalism).

  2. However, there exists various approaches to manifest Lorentz-covariant Hamiltonian formalism, see e.g. this and this Phys.SE posts.

  3. Comments 1 & 2 also apply to gauge theories & BRST formulations.

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