Re: What is locality in quantum field theory?

From: Chris Oakley (coakley_at_cgoakley.demon.co.uk)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 19:00:55 +0000 (UTC)

> But this brings me to my question. What exactly do we mean by locality?
> In quantum field theory, locality doesn't apply to states, but instead,
> to the operators (fields) acting upon the states. This most definitely
> does not agree with what we expect of locality, of what we think
> locality is. If we interprete the formalism of quantum field theory
> literally, it means we can't say "this thing is here", but only "the
> operator measuring the existence of this thing here is localized here".

Indeed. One problem is that the field operator contains both "creation" and
"annihilation" operators.

The creation part, which creates the physical states, can be extracted with
the convolution

\phi_{+}(x) = \int d^4x' C(x-x') \phi(x')

Where C(x) = (2\pi)^{-4} \int d^4p \theta(p_0)\theta(p^2) e^{-ip.x}

- but this is a non-local construction which will no longer in general
commute or anticommute with similar operators for spacelike intervals.