Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

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

I often see that action is written with a Euclidean metric instead of the original Minkowski metric. My question is basically this : Under what conditions is okay to make a wick rotation? I am thinking of the Wick-rotation in a manner analagous to a change of contour in a contour integral. In the case of contour integral, before making a similar change in contour, I would consider issues like location of poles of the integrand, behavior of the integrand at infinity of the complex plane etc. But in case of Wick rotation, I don't see such things discussed.

I would appreciate if some of you could answer or give some inputs to answer the following questions I have:

Is the rotation just as trivial as a change of variable : $\tau=\imath t$ ?

How do I know that the rotation should be $\tau=\imath t$ and not $\tau=-\imath t$

Can I always make a wick rotation for any Lagrangian?


EDIT/PARTIAL-ANSWER/GENERAL-UPDATE: sheds some light on the issue. The short section on lack of an analytic continuation tells me that in a general case wick rotation needs to be justified.

share|cite|improve this question
Are you considering flat or curved spacetime? – Valter Moretti Feb 25 '14 at 18:21
I think it is just an analytic continuation. It connect propagator and partition function of one system. For $\tau=it$, it gives the partition function directly, but $\tau=-it$ does not. – qfzklm Feb 25 '14 at 18:57
I was thinking of flat space. – symanzik138 Feb 25 '14 at 21:53

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.