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Jon Lester
Posted: Wed Mar 21, 2007 5:11 am
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I have read some recent accounts about the scalar field theory (\lambda
\phi^4) in four dimensions. There exist, mostly due to Luescher and
Weisz, strong clues that this theory in four dimensions should be
trivial. This means that the propagator should take the form

G(p)=A/(p^2+mr^2)

being A a constant and mr a renormalized mass. Indeed, the situation
is not that easy as recent papers by Stevenson and Weisz claims that a
proper fit in the symmetrical phase should be

G(p)=A/(p^2+mr^2)+B/(p^2+(3mr)^2)

and in the broken phase

G(p)=A1/(p^2+mb^2)+B1/(p^2+(2mb)^2).

Does this means that other similar corrections could be involved in
this Green functions? Would it be difficult to check this? Does all of
this mean that the concept of triviality, while true, should be
properly redefined?

Jon
 
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