Question

Is static gauge quantization of the particle equivalent to covariant quantization?

Answer 1

In the covariant quantization one is able to get directly (from the constraint pμμ+m2=0pμμ+m2=0) the Klein-Gordon equation. But if one uses the parametrization τ=X0τ=X0 then the Schrodinger equation is not local anymore (the reason is the square root in the hamiltonian).

I think it has to do with antiparticles. So my guess is that covariant quantization is equivalent to light-cone quantization but it is not equivalent to static gauge quantization

Answer 2

We will now turn to the problem of the quantization of gauge theories. We .... Consider for instance a particle of mass m moving freely ...