  Time-independent gauge transformations are implemented in the canonical
formalism by the Gauss law which is not covariant. The covariant form of Gauss
law is conceptually important for studying asymptotic properties of the gauge
fields. For QED in $3+1$ dimensions, we have developed a formalism for treating
the equations of motion (EOM) themselves as constraints, that is, constraints
on states using Peierls' quantization. They generate spacetime dependent gauge
transformations. We extend these results to the Maxwell-Chern-Simons (MCS)
Lagrangian. The surprising result is that the covariant Gauss law commutes with
all observables: the gauge invariance of the Lagrangian gets trivialized upon
quantization. The calculations do not fix a gauge. We also consider a novel
gauge condition on test functions (not on quantum fields) which we name the
"quasi-self-dual gauge" condition. It explicitly shows the mass spectrum of the
theory. In this version, no freedom remains for the gauge transformations: EOM
commute with all observables and are in the center of the algebra of
observables.
