Re: Why do we need quantum fields in QED?

In message <4339DFFF.1070703@xxxxxxxxxxxx>, Eugene Stefanovich
<eugenev@xxxxxxxxxxxx> writes
>
>
>Charles Francis wrote:
>> In message <4329CDEA.8050902@xxxxxxxxxxxx>, Eugene Stefanovich
>> <eugenev@xxxxxxxxxxxx> writes
>> [snip]
>> What you describe is essentially correct, and is used as the basis
>>of
>> what JB once called "naive" treatments of QED. I have put a lot of work
>> into making it rigorous. The fundamental problem is that you can carry
>> out a discrete construction pretty much exactly as stated, but a
>> discrete construction does not obey manifest covariance. If you try and
>> take the limit and move over to a continuum in order to recover
>> covariance, the theory breaks down in the Landau pole.
>> I have a paper on discrete qed, but the real issue is not whether it
>>is
>> a sound mathematical construction, but whether it is valid as a physical
>> model. This actually depends on one's philosophical stance re the
>> meaning of covariance and the nature of physical measurement. In order
>> to establish that a discrete model is physically legitimate I have
>> written a paper, gr-qc/0508077, currently being refereed which, imv,
>> pretty much does the job. It also makes some unexpected predictions in
>> cosmology, so hopefully it is testable.
>
>Thank you for the reference, but I suspect we are talking about
>different things. I was referring to the standard QED in which
>positions can be measured with unlimited precision and the spectrum of
>the position operator is continuous.

Yes. Then the problem is, as I say, that the theory breaks down in the
Landau pole. It is inconsistent, and therefore it must be wrong.

What I was saying is that in order to create a theory like this using a
continuum one should formulate it using a finite lattice and let lattice
spacing go to zero. The simple answer to your question is that the limit
does not exist.

> The theory I had in mind has
>full relativistic invariance: the interacting generators of the
>Poincare group form a representation of the Poincare Lie algebra
>as in S. Weinberg "The quantum theory of fields", vol. 1
>eqs. (3.3.11) - (3.3.17).
>
>Eugene.
>
>



Regards

--
Charles Francis

.

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