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

*From*: david+news@xxxxxxxxxx (David Madore)*Date*: Thu, 1 Oct 2009 19:07:51 +0000 (UTC)

"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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**References**:**Re: QFT: is there a "multi-time" (Lorentz-invariant) Fock space?***From:*Juan R. González-Álvarez

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