Re: Spontaneous particle-antiparticle pair production

whopkins_at_csd.uwm.edu
Date: 03/23/05 

Date: Wed, 23 Mar 2005 10:34:03 +0000 (UTC)

>>From the Postman:
>is there any possibility that more than one [pair production] can
occur
>at the same point and time. And if this was possible how would
>multiple events react to each other

When doing calculations in S-matrix theory using the Wick time ordering
in the perturbation expansion, the effect of this time ordering is to
cluster things pairwise. In effect, this limits interactions to only
two at a time.

When doing renormalization -- as is best seen in the Epstein-Glaser
picture, what you're actually doing is substituting the ill-defined
time ordering operator by one that has consistent properties. Among
its other features is that it clusters larger groups together than just
two at a time.

But in a renormalizable theory (indeed, the essence of the very
definition) the clusterings do not lead to anything qualitatively
different than what's already there to start out with. Generally, in
the most general situation, it would lead to the creation of effective
interactions, each in effect represented by a single term in the
corresponding field theoretic Lagrangian. Each melded process is --
for all practical purposes -- the combination of two or more basic
processes occurring together.

The very reason for the original divergence in the original time
ordering operator, and in the perturbation theory defined through it,
was that it did not take correctly into account the effect of two or
more things going on at the same place and same time. That's what the
regularization done by Epstein-Glaser does and why everything remains
finite and well-defined in the corresponding calculations at each order
in the perturbation theoretic expansion.

On the larger question: no fermions don't touch each other. A direct
fermion-fermion interaction, in fact, is non-renormalizable. Instead,
they interact through bosons, and only through bosons -- and bosons can
touch each other and stack up ad infinitum at the same place.

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