All Questions
21
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How is Wick rotation an analytic continuation?
Wick rotation is formally described by the transformation
$$t \mapsto it.$$
In many place it is stated more rigorously as an analytic continuation into imaginary time. I understand why we do it but ...
- 3,350
1
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0
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178
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Time-Ordered Propagator in Euclidean Space
I saw a paper stating that in Euclidean signature, the Feynman propagator $G_E$ is related to the Wightman functions $W_{\pm}$ via
$$
G_E (x) = \Theta(\tau) \, W_+ (x) + \Theta(-\tau) \, W_- (x) \, ,\...
- 21
1
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0
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45
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Physics in Euclidean spacetime [duplicate]
I just have a very small and naive Question.
In my PhD I work on different Toy models which are implemented on the lattice.
In order to do so one performs a Wick rotation from minkowski to euclidean ...
- 11
6
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319
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Schwinger-Keldysh contour and $i\epsilon$ prescription
In Tom Hartman's notes on path integrals, he describes the Schwinger-Keldysh (or "in-in") formalism for calculating vacuum correlators in QFT.
He explains that Lorentzian time-ordered vacuum ...
- 1,455
15
votes
2
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1k
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Feynman diagrams, can't Wick-rotate due to poles in first and third $p_0$ quadrants?
I have a confusion about relating general diagrams (involving multiple propagators) in Minkowski vs Euclidean signature, which presumably should be identical (up to terms which are explicitly involved ...
- 5,371
5
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1
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504
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How does the $+i\varepsilon$ prescription in the propagator comes from analytic continuation of the Euclidean 2-point function?
Let $S_0[\phi]$ be the action for a real Klein-Gordon field $$S_0[\phi]=\dfrac{1}{2}\int d^Dx \phi(x)(\Box-m^2)\phi(x)\tag{1}.$$
If we try to construct the generating functional $Z_0[j]$ we find that ...
- 36.4k
2
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0
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145
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How to analytically continue Schwinger functions?
To get Wightman functions $W(t_1, \dots, t_{k-1})$ from Schwinger functions $S(\tau_1 = i t_1, \dots)$, we use analytical continuation.
But I don't think this is simply an issue of plugging $it_a$ for ...
- 16.2k
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1
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94
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Complex time theories with spacetime $\mathbb{R}^3\times\mathbb{C}$
Are there any well-developed (string?..) theories assuming that, what we perceive as a (3+1) Minkowskian manifold, is a projection/compactification of a 5-dim spacetime, locally obtained via ...
- 2,921
2
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1
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143
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Can you perform a Wick rotation if the poles are on the imaginary axis?
I know you can perform a Wick rotation whenever the poles are outside the contour but what happens if the poles are on the imaginary axis? Can you do it anyway?
- 23
5
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3
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555
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Why can you deform the contour in the integral expression for the Klein-Gordon propagator to get the Euclidean propagator?
I'm trying to understand the use of the Euclidean correlation functions in QFT. I chased down the problems I was having to how they manifest in the simplest example I could think of: the two-point ...
- 188
4
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0
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95
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Analytic Continuation: Replacement of $t \rightarrow - i \tau$ Mathematical Justification [duplicate]
It's commonly used in imaginary-time path integral that "analytic continuation" means replacing $t \rightarrow - i \tau$ or reparametrizing the theory in terms of imaginary time $\tau = i t$....
- 83
4
votes
2
answers
681
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Wick Rotation & Scalar Field Value & Mapping
Wick Rotation helps to solve the problem of the convergence of the path integral, by changing the integral contour in the complex plane. But my question is:
In the scalar field path integral, the ...
- 51
6
votes
2
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2k
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Wick rotation: still trouble in getting how it works
I'm preparing my second exam in QFT and I still have trouble in getting the Wick rotation and its analytic continuation. I know that this topic have been discussed a lot in previous threads, but I ...
- 61
1
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1
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146
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Can conformal transformations in $\mathbb{R}^{1,1}$ be analytically continued to $\mathbb{R}^{2,0}$?
In 1+1 dimensions, 2D Minkowski space, a conformal transformation is given by two real functions (of one variable). After Wick rotating the time dimension, giving us 2 dimensional Euclidean space, ...
- 11.6k
4
votes
2
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975
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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 ...
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