Re: dose tree-level results in effective potential incorporate loop effects?

On 2005-05-23, beacon <noncommutate@xxxxxxxxxxxx> wrote:
> For a Lagrangina, we can perform the one loop calculations and
> renormalization to get the one loop results. If we have the one-loop
> effective potential, can we perform tree level calculations with this
> potential to get the same loop results in the original theory?
> I think we still have to do one loop calculation with the effective
> potential to get one-loop results of the original theory. Is this
> right?

No, you only need tree diagrams from the effective potential. The reason
comes down to the fact that the amplitude of a vertex of the effective
potential is defined to be the sum of all possible amplitudes with the
same external legs of the original potential. If you can't calculate all
such amplitudes, then just replace "all possible " by say "all possible
one-loop".

Weinberg, QFT vol.2, Ch.16, top of page 66.

Igor

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