# A Local degrees of freedom and correlator

1. Oct 7, 2016

### spaghetti3451

In quantum field theory, the degrees of freedom $\phi({\bf{x}},t)$ are local. This means that the the dynamics of the field in a given region of spacetime is not governed by events outside its lightcone.

Is the local/non-local nature of degrees of freedom in a quantum field theory independent of the second quantisation of the classical fields in the theory to quantum fields?

Is the local/non-local nature of degrees of freedom in a quantum field theory independent of the transition from, for example, the time-ordered vacuum expectation value

$\langle \Omega | T\{q(t_{1})\cdots q(t_{n})\}|\Omega\rangle = \frac{\int\mathcal{D}q(t)\ e^{iS[q]}q(t_{1})\cdots q(t_{n})}{\int \mathcal{D}q(t)\ e^{iS[q]}}$

in quantum mechanics to

$\langle \Omega | T\{\phi(x_{1})\cdots q(x_{n})\}|\Omega\rangle = \frac{\int\mathcal{D}\phi(x)\ e^{iS[\phi]}\phi(x_{1})\cdots \phi(x_{n})}{\int \mathcal{D}\phi(x)\ e^{iS[x]}}$

in quantum field theory?

Does the local nature of a field theory manifest itself only in the action of the theory?

2. Oct 12, 2016

### Greg Bernhardt

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.