# 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