Re: QFT: is there a "multi-time" (Lorentz-invariant) Fock space?



"Juan R. González-Álvarez" in litteris
<pan.2009.09.29.11.20.30@xxxxxxxxxxxxxxxxxxxx> scripsit:
David Madore wrote on Thu, 24 Sep 2009 20:05:51 -0400:
Does this last remark remark to sections S6g and S9c of Arnold
Neumaier's FAQ at <URL:
http://www.mat.univie.ac.at/~neum/physics-faq.txt >?

Someone recommended you to read the FAQ *before* continuing posting.

I did. That's the reason why, for example, I suggested to limit my
questions to the (1+1)-dimensional case, where mathematically rigorous
theories exist.

If one reads the index, one would find entries for sections as

S6d. Is there a rigorous interacting QFT in 4 dimensions?

S7c. Bound states in relativistic quantum field theory

The answers don't always enlighten me. Or rather, I understand
something of what they say, but I don't understand how various
problems relate. In your answer to Bob_for_short (in message
<pan.2009.09.29.11.21.04@xxxxxxxxxxxxxxxxxxxx>) your write that "the
no-interaction theorems, has little to see with renormalization and
self-action troubles", so now I'm very confused. Could you explain
what the relations are between:

(a) the difficulties involved in renormalization (which seem to get
worse as dimension increases?),

(b) the difficulties involved in constructing theories satisfying the
Wightman axioms (which also seem to get worse as dimension
increases?), discussed in section S6d of the FAQ,

(c) the difficulty (impossibility?) to write partial differential
equations for the interacting fields, which you mentioned,

(d) the difficulties with interpolating field, discussed in section
S6g of the FAQ

? How are these problems connected? And, in particular, which
"problems" (of any kind) still exist or remain for a simple
(1+1)-dimensional scalar field with a \phi^4 term in the Lagrangian?

--
David A. Madore
( http://www.madore.org/~david/ )
(Do _NOT_ remove the "+news" extension to email me.)

.



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