Re: When do we need renormalization

From: Eugene Stefanovich (eugenev_at_synopsys.com)
Date: 12/28/04 

Date: Tue, 28 Dec 2004 19:54:54 +0000 (UTC)

Arnold Neumaier wrote:
> Eugene Stefanovich wrote:
>
>>Arnold Neumaier wrote:
>>
>>
>>>Eugene Stefanovich wrote:
>>>
>>>
>>>
>>>
>>>>I think these views are prevailing at the moment. My work on RQD,
>>>>however, shows that all renormalization problems can be solved without
>>>>such an assumption, and a consistent theory of charged particles and
>>>>photons can be constructed on its own without any reference to
>>>>something "more fundamental".
>>>
>>>You are claiming far too much.
>>>
>>>You haven't shown your theory to be consistent. You only constructed a
>>>sequence of approximate Hamiltonians with neither Lorentz invariance
>>>nor gauge invariance. Consistency would require that you can show
>>>that a limiting Hamiltonian exists which gives rise to a theory
>>>having both these properties.
>>>
>>>Arnold Neumaier
>>
>>I have said repeatedly that I agree with you.
>
>
> If you'd really agree with me you'd moderate your claims.
> You claim to have a 'consistent theory of charged particles and
> photons' which you do not have, unless you use the term 'consistent'
> in a very loose and misleading way.

I agree to moderate my claims in the sense that I do not have
the proof of convergence. Otherwise, in each particular order
the construction is exact and avoids inconsistencies characteristic
for QFT, such as ultraviolet divergences.

>
>
>
>>I do not have
>>a proof that the series for the Hamiltonian converge. Just as
>>traditional QED does not have a proof that the series for the
>>S-matrix converges.
>
>
> Without having a Hamiltonian, you do not have a Hamiltonian theory
> of QED, and not even an S-matrix. What you have is a sequence of
> Hamiltonians H_k and a corresponding sequence of dynamical theories,
> of which you can prove that the corresponding S-matrices S_k agree
> to order O(alpha^k) or O(hbar^k) with the S-matrices of QED.

I disagree here: the k-th order S-matrix computed with k-th order
RQD Hamiltonian coincides exactly with the k-th order S-matrix of
renormalized QED (not to order O(alpha^k), but exactly!).

Eugene Stefanovich.

>
> But doing dynamics with some H_k probably drives you away from the
> true dynamics of QED in a very short time...
>
>
> Arnold Neumaier
>

Relevant Pages

  • Re: When do we need renormalization
    ... Arnold Neumaier wrote: ... > You haven't shown your theory to be consistent. ... a proof that the series for the Hamiltonian converge. ... Eugene Stefanovich. ...
    (sci.physics.research)
  • Re: Finite time calculation in QED
    ... Eugene Stefanovich wrote: ... > Arnold Neumaier wrote: ... >>If the Hamiltonian is H then ... >>as always in quantum mechanics. ...
    (sci.physics.research)
  • Re: Connes & Marcolli paper on renormalization
    ... Arnold Neumaier wrote: ... > Eugene Stefanovich wrote: ... I don't see how Hamiltonian can be finite when parameters e and m ... turn out to be infinite after renormalization. ...
    (sci.physics.research)
  • Re: Connes & Marcolli paper on renormalization
    ... Eugene Stefanovich wrote: ... The perturbation series for the renormalized S-matrix does not ... Hamiltonians of the textbook kind, your series for the Hamiltonian might ... Arnold Neumaier ...
    (sci.physics.research)
  • Re: How real are the "Virtual" partticles?
    ... > Instead of the Hamiltonian one can also have the action. ... > some experimentalists would probably be motivated to push for a ... dynamical predictions were compared with experiment. ... Eugene Stefanovich. ...
    (sci.physics.research)