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# Questions tagged [wick-rotation]

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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### Dirac equation without $i$

In Witten's review paper "Fermion path integrals and topological phases", the Dirac equation (Eq(2.2)) is $$(\gamma^{\mu}D_{\mu}-m)\psi=0$$ which appears very strange to me. Initially I thought this ...
204 views

### The way momentum space integrals tend to infinity

At the beginning of chapter 15 of Schwartz, he states that $$\int d^4k \frac{k^2}{k^4}=\int \frac{d^4k}{k^2}\sim \int k\ dk.$$ I don't see how he got this at all. Isn't this just the integral \...
216 views

### Using Wick Rotation to calculate Generating Function in Minkowski Space

The question arises when I'm reading over the section "3.3.1 Minkowski Space" in page 16-17 in the following link: https://www-thphys.physics.ox.ac.uk/people/JohnCardy/qft/qftcomplete.pdf It is ...
39 views

### Convergence of the path integral

In P&S 9.3 the path integral $$Z[J]=\int {\cal D}\phi \exp[i\int d^4x ({\cal L} + J\phi)]$$ of the (Minkowski) $\phi^4$-theory when subjected to a Wick-rotation (change of the integration path ...
345 views

### What is the proper definition of Schwinger functions?

In the book Mathematical Aspects of Quantum Field Theory (2010) on page 159-160 in chapter 6.6 Wick rotations and axioms for Euclidean QFT the following is stated: We have seen earlier in this ...
28 views

### Can there exist a contrived case for the Wick rotation in position space to be meaningful?

Question So this is a complementary question to this. From the answers it seems can't one use a Wick rotation of position to create something physically meaningful. Does this hold even in contrived ...
196 views

### In light of Wick rotations is position and time on the same footing in QFT?

Taken from here Wick rotation connects statistical mechanics to quantum mechanics by replacing inverse temperature $1/(k_{B}T)$ with imaginary time $it/ℏ$ But I was under the impression position ...
6k views

### Minkowski Metric Signature

When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ds^{2} = -(c^{2}dx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2}$$ ...
66 views

### Confusion about gamma matrices in Euclidean spacetime

I have encountered a number of sources with differing definitions of the transition from Minkowski spacetime to Euclidean spacetime. I'd like some clarification as to how to go from Minkowski to ...
205 views

### Rewriting bosonic action in Altland and Simon Chapter 4

In page 179 of Altland and Simon, Condensed Matter Field Theory, the author obtained the action \begin{equation} S[\theta]=\frac{1}{2\pi}\int dx\,d\tau\,\left[(\partial_x\theta)^2+(\partial_\tau\...
39 views

### “Imaginary-time” argument in high energy physics

In many-body physics, there are many "imaginary-time" techniques, such as Matsubara Green's function, imaginary-time path integral and others. It seems that these concepts are frequently used in ...
5k views

### Schrödinger equation derivation and Diffusion equation

I am aware of the debate on whether Schrödinger equation was derived or motivated. However, I have not seen this one that I describe below. Wonder if it could be relevant. If not historically but for ...
352 views

### Wick rotation - time and what else changes?

For aid of example consider two quantities the four-momentum $\tilde P$ and a time-independent four potential $\tilde A$. Now if a wick's rotation was carried out by simply replacing $it$ with $\tau$ ...