Faddeev-Popov Ghosts in the canonical formalism

Question

In the Lorenz gauge in electrodynamics, the timelike and longitudinal components can be eliminated by prescribing the Gupta-Bleuler condition $\partial^{\mu}A_{\mu}|\Psi\rangle=0$ 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?

Answer 1

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.