- #1

- 34

- 0

this is quite a basic question I know, but something I'm not sure I've fully got my head around. In classical particle mechanics the dynamical variable is the position vector x, and in classical field theory the dynamical variable becomes the field [tex]\phi(x) [/tex], with x being relagated to just a label to each of the infinitity of these dynamical variables [tex]\phi[/tex] at each point in space if you like.

Then in regualar QM, the things that were dynamical variables in classical particle mechanics (position, momentum etc...) get promoted to operators, with the actual states being abstract vectors in the hilbert space of these operators. In QFT the dynamical variable from classical field theory, the field itself, gets promoted to an operator. But what are the analogues of the eigenvalues of position/momentum/angular momentum etc from regualar QM?

Also I noticed that in QM the solutions of the Schrodinger equation are the actual states themselves, but in QFT the solutions of the KG eqn or the Dirac equation say, are the field operators not the states. So what are the actual states? are they somehow abstract vectors of the field operators?