This question resulted, rather as by-product, the discussion on how to count degrees of freedom (DOF). I extend that question here:
- Are necessary1 derivatives such as velocities counted as individual DOFs or together with the respective coordinate2?
- Should complex valued DOFs be counted twice as in "two real-valued DOFs" or once as in "one complex-valued DOF"? (I mean, when one does not want to specify this explicitly)
Please answer with some reference, unless it turns out this is actually a matter of taste rather than a strictly defined thing.
1) I mean those a value of which is required as an initial condition
2) I count fields in QFT as coordinates as well, while space-time-coordinates are parameters to me, if that matters. I know a field actually has $\infty$ (or rather, $2^\aleph$) DOFs itself, but let's say e.g. "one $\mathbb R^3$ continous DOF" in that case