Re: Renormalization

From: Eugene Stefanovich (eugenev_at_synopsys.com)
Date: 03/19/05 

Date: Sat, 19 Mar 2005 08:03:28 +0000 (UTC)

Chris Oakley wrote:
>>I believe that one day we'll find truly
>>fundamental first principles which would allow us to formulate
>>the finite dressed particle Hamiltonian directly without any
>>involvement of gauge quantization, renormalization, and dressing.
>>In my opinion, these "first principles" should contain the following three:
>>1) relativistic invariance == Poincare commutators between the
>>Hamiltonian, boost, and other generators;
>
>
> Agreed.
>
>
>>2) instant form of relativistic dynamics == interaction terms in
>>the Hamiltonian and boost operator only;
>
>
> I don't believe in the existence of an interaction part of a Hamiltonian, or
> anything else that violates Haag's theorem, except as an approximation.

I don't believe in the Haag's theorem. There is nothing wrong with the
theorem and its proof, but I don't think the statement of the theorem
has any connection to physics, because I do not believe that
quantum fields have any physical meaning. I find free quantum fields
to be a useful mathematical tool for building relativistically invariant
Hamiltonians. However, I don't find any place in theory for interacting
quantum fields (all predictions of interacting theory can be formulated
without using interacting fields at all, the Hamiltonian is enough).
Haag's theorem insists that when you use the interacting Hamiltonian
H = H_0 + V
then there is no "local interacting quantum field
with manifestly covariant transformation properties". I do not care,
because in my view the thing I put in quotes does not belong to physics.

>
>
>>3) full dressing == interactions do not act on zero-particle
>>(vacuum) and one-particle states.
>
>
>
> This is a big problem I have with the traditional, Haag-theorem-violating
> way of doing QFT. The vacuum should just be the zero particle,
> Poincare-invariant state whether there are interactions or not. The idea
> that the vacuum not being this (e.g. being full of virtual
> particle/antiparticle pairs) seems wrong to me almost by definition.

I agree 100%. That's exactly why I like the dressed particle approach
so much. It does not have these terrible problems.
The interaction operators are such that they do not act
(= yield zero when acting) on vacuum and one-particle states.
So, vacuum is just a zero-particle state whether there are interactions
or not. One-particle states contain just 1 particle and are eigenstates
of the full Hamiltonian with experimentally observed masses.

>
>
>>As far as I know, these 3 principles are not enough for
>>formulating a full dynamical theory. There should be something else
>>which I do not know.
>
>

Relevant Pages

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