Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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. – Sidious Lord Mar 4 '12 at 15:46
@SidiousLord: good point. But I'm more interested in seeing an application in a specific problem, which Weinberg's book hasn't done. – felix Mar 4 '12 at 18:10
it would be easier to realize that Instantons are tunneling solutions to the physical Minkowski theory, and that the Euclideanization is a trick to streamline the WKB method in field theory. – QuantumDot Aug 26 '12 at 14:24

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.