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In what sense are loop diagrams quantum corrections?

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What's so not-quantum about tree-level diagrams?

This post has been migrated from (A51.SE)
asked Dec 18, 2011 in Theoretical Physics by dbrane (375 points) [ no revision ]
From the tag of the question, you are already assuming "FIELD" theory, are you? So the queston is how classical the fields are?

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2 Answers

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The reasons were given here. Essentially, at tree level you recover classical results. Loop corrections are proportional to powers of $\hbar$ and these are quantum terms.

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answered Dec 18, 2011 by JonLester (376 points) [ no revision ]
That is right, but classically spin does not exist and so, the result is consistent.

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It is a bit more obscure for particles with spin, because then the classical result has still an $\hbar$.

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Tree level diagrams are one-particle relativistic quantum mechanics, but not quantum field theories.

The point is obscured by two reasonable details in modern QFT books: they avoid to speak of "2nd quantisation", and they set h=1 everywhere (so for instance it is not so clear how different the h->0 limit is for fermions than for scalar fields, or how bosons can add to build a classical electromagnetic field but fermions can not). It is expected that you go across a relativistic quantum mechanics textbook before jumping to QFT, but sometimes the career path is different.

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answered Dec 19, 2011 by anonymous [ no revision ]
There are relativistic quantum mechanics textbooks that are not quantum field theory texts?

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