I am self-studying dynamics of constrained systems and their quantisation from Rothe and Rothe book "classical and quantum dynamics of constrained systems". While using Dirac quantisation, we can implement second class constraints using Dirac bracket and then we say as we are interested in the dynamics of observables, so we can even fix gauge freedom without affecting the E.O.M of observables so along with first class constraints and second class constraints we also implement gauge fixing conditions from which we can have a Dirac-star bracket calculated by considering all constraints and gauge conditions which is then promoted to quantum commutator.
My question is why are we bothering about secondary constraints (can be first class or second class) as they are obtained from time persistence condition and thus uses classical E.O.M, which intuitively should not survive quantisation. Even in path integral approach to constrained dynamics, we tend to implement all constraints and gauge conditions without bothering about secondary constraints. In this again we should ignore secondary constraints as they are resultant from E.O.M. I don't know where I am making wrong conclusions.
I referred to the below answer but did not got satisfaction with this: How are second-class constraints handled in the path integral formulation? I even read the Senjanovic paper - Senjanovic, P. (1976). Path integral quantization of field theories with second-class constraints. Annals of Physics, 100(1-2), 227–261. doi:10.1016/0003-4916(76)90062-2, but he also don't discuss this.
Any pointer to the literature or a brief discussion here will be of great help.
