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Why can we get away with this? It seems mathematically we have to include counterterms in the classical solution for a saddle point expansion to be valid.

- Thread starter geoduck
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- #1

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Why can we get away with this? It seems mathematically we have to include counterterms in the classical solution for a saddle point expansion to be valid.

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atyy

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So if we write [itex]\lambda=k*\frac{1}{\hbar c}[/itex], where k is a pure number, then whether your higher order perturbative terms are small compared to tree level depends on the value of the pure number k, and not on Planck's constant.

So for example, the one-loop 4-pt function is [itex]\lambda+k*\lambda^2\log\left( \frac{E}{\mu}\right)*(\hbar c) [/itex].

I assume that [itex](\hbar c)[/itex] is in the one-loop correction to make the dimensions of the two terms the same. With n-loops I assume you'll get [itex](\hbar c)^n[/itex]. But you can't say this is small, because you'll also get [tex]\lambda^n [/tex], which has units of [itex](\hbar c)[/itex] in the denominators.

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