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Instantons and Borel Resummation

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As explained in Weinberg's The Quantum Theory of Fields, Volume 2, Chapter 20.7 Renormalons, instantons are a known source of poles in the Borel transform of the perturbative series. These poles are on the negative real axis, and the series remains Borel-summable as long as the coupling constant is not too large.

However, instantons are objects in the Euclidean version of QFT. What's the significance of the above Borel resummation in the Minkowski theory?

This post has been migrated from (A51.SE)
asked Mar 4, 2012 in Theoretical Physics by felix (110 points) [ no revision ]
retagged Jan 1 by Dilaton.admin
@SidiousLord: good point. But I'm more interested in seeing an application in a specific problem, which Weinberg's book hasn't done.

This post has been migrated from (A51.SE)
You seem to be thinking that the perturbation theory of the Euclidean and Minkowskian theories are unrelated, but in fact they are related. I suppose a good analogy here is complex analysis, where you can compute an integral by contour deformation and the position of the poles in complex plane is important.

This post has been migrated from (A51.SE)

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