# Commutators and the Parametric Nonrelativistic Particle?

1. May 31, 2007

### Angryphysicist

OK, I'm a wee bit sleep deprived and cannot recollect some facts about the Dirac quantization of gauge theories. With the quantization of the parametrized nonrelativistics particle, do we still change the Poisson bracket into commutators?

More specifically, for the non-relativistic particle, would the following hold:
$$i\hbar\dot{x} = [x,H]$$

If not how can I find the velocity operator for the parametrized nonrelativistic particle?

Thanks for all the help!

: I suppose my real question is: Can I still use the Heisenberg picture with the Dirac Quantization of First Class Constrained gauge systems?

Last edited: Jun 1, 2007