# Tagged Questions

Wick rotation substitutes an imaginary-number variable for a real-number time variable to map an expression or a problem in Minkowski space to one in Euclidean space which are easier to evaluate or solve. Use for all types of rigid analytic continuation maps.

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### Invariance in Euclidean and Minkowski spaces

Consider Wick's rotation from Minkowski to Euclidean space in QFT. What is the connection between O(4) invariance in Euclidean space and Lorentz invariance in Minkowski space? If we define a quantity ...
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### Conditions permitting rotation to imaginary time

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 ...
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### Relationship between the Black-Scholes model and path integrals

This question was inspired by some interesting comments by Rod Vance on this answer. Could you (Rod), or someone else, expand on these comments and give a brief summary of the connection between the ...
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### Does anybody know of a source that explains Wick rotation for fermions in 3-dimensional spacetime?

I've been looking for a long time and I've not had a lot of luck. I've found sources that use fermions in 3d Euclidean space but I can't find any that explain the Wick rotation from Minkowski space. ...
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### What is the Levi--Civita connection of a Wick rotated metric?

A Wick rotation is a transformation that allows to change from a Lorentzian manifold to a Riemaniann manifold. In the cases when this is possible, is the Levi-Civita connection of the Riemaniann ...
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### Is Wick rotation invariant under proper conformal transformations?

Is Wick rotation invariant under proper conformal transformations? Why or why not? Does Wick rotation apply to conformal field theories? $(1-i\epsilon )T$ is not invariant under proper conformal ...
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### Wick rotation for FRW in quantum gravity

There is no timelike Killing vector for FRW cosmologies. In the path integral formalism, is it possible to Wick rotate for quantum cosmology in quantum gravity? If yes, how? If no, how does one work ...
### $\mathrm{i}\epsilon$ prescription makes a function analytical?
I've seen this everywhere where they say "Analytic continuation is obtained by the usual $\mathrm{i}\epsilon$ prescription..." but how is that? How do you analytically continue (say) $\ln x$ with ...