Re: nonlinearities in QFT

From: Arnold Neumaier (Arnold.Neumaier_at_univie.ac.at)
Date: 09/28/04 

Date: Tue, 28 Sep 2004 16:50:46 +0000 (UTC)

Blake Winter wrote:
> But don't we see LQG attempting to evolve from one spin foam as a
> starting point to another?

I don't know about hypothetical theories like LQG.
I was talking about the verifiable and verified consequences of
relativistic QFT, as revealed by calculations for QED, QCD, and the
standard model.

> And can't we use path integrals to evolve
> from one field configuration to another?

The problem with path integrals is that they are formal objects without
a clear meaning; whatever one tries to compute with them turns out to be
infinite. Only selected objects derived from path integrals can be given
meaning by means of the renormalization procedure. The books show how to
give meaning to S-matrix elements between asymptotic in and out states.

But I haven't seen a single article that gives meaning (i.e., finite,
renormalization scheme independent results) to, say, QED states at
finite t and their propagation in time.

> Then by starting with some
> Psi over the initial configurations we will be able to evolve it in
> time, right? I guess I'm wondering why its not true that the dynamics
> are properly defined.

People don't even know what an initial configuration Psi should be
(i.e., from which space to take the states at finite t) in a
relativistic QFT; so how can they know how to propagate it...

Arnold Neumaier

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