Re: Dirac on renormalization

Eugene Stefanovich wrote:
>
> Arnold Neumaier wrote:
>
>> The concept of bare particles (and infinite masses and coupling
>> constants) does not figure at all in modern settings of renormalization
>> based on the renormalization group. (See, e.g., Salmhofer's book).
>>
>> Thus these worries are no longer relevant.
>
> We discussed this a lot, but I am still puzzled by your words.
> Let me take for definiteness the expression (11.1.1) from Weinberg's
> vol. 1.

If you want to have precise statements, you must look into the
literature on mathematical physics, not into Weinberg who proceeds
with lots of handwaving and uses the traditional fuzzy motivations to
which physicists are accustomed. I am tired of repeating old things
to deaf ears.

> If the above statements are true, then does Salmhofer's book address
> these problems? If yes, then I should definitely get a copy.

You should definitely get a copy. He does renormalization theory without
ever mentioning bare particles or infinities in the formal exposition.
Everything he does is mathematically sound. He constructs the expansion
of the S-matrix with the same rigor as one constructs the expansion of
the exponential function in undergraduate math.

Arnold Neumaier

.