- #106
DrDu
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Has this argumentation on anomaly freeness also been formulated in a non perturbative setting like algebraic qft or does there exist a soluble toy model?
DrDu said:Has this argumentation on anomaly freeness also been formulated in a non perturbative setting like algebraic qft or does there exist a soluble toy model?
Fujikawa's method is nonperturbative since it uses directly the path integral itself, not Feynman diagrams. However it is not rigorous for two reasons:tom.stoer said:I think that in principle it should be possible to formulate the Fujikawa method non-perturbatively.
DarMM said:Exactly, in a sense Strocchi's theorem isn't really that surprising. Even Strocchi himself in some of his books makes this point, also see the book by Steinmann "Perturbative QED and Axiomatic Field Theory".
[...] So Strocchi and others such as Nakanishi show that the Gupta-Bluer condition and ghosts arise from trying to work with a field as "Wightman-like" as we can manage.
I don't think Strocchi is really pointing anything out, more just showing where naïve assumptions from formal field theory go wrong and what is really going on behind the scenes.
kexue said:The OP droped out long ago.
and doesn't seem to have further questions.mathman said:There is a long ongoing discussion in this forum on this subject (I started it it).
tom.stoer said:Solving this consistency conditions results (besides other physical predictions) in a relation saying
q(u) = 2/3 q(e)
q(d) = -1/3 q(e)
where the 1/3 is due to the fact that each quark is counted three times b/c it exists in three different colors. That means that due to these algebraic relation q(proton) = -q(electron).
I'll put together a reply. It is taking some time because your question has a very deep answer, linking into the nonperturbative definition of the Higgs phenomena.DrDu said:As yet I got no reply to my posting #111, ...
DarMM said:I'll put together a reply. It is taking some time because your question has a very deep answer, linking into the nonperturbative definition of the Higgs phenomena.