All Questions
9
questions
1
vote
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
$$
G_E (x) = \Theta(\tau) \, W_+ (x) + \Theta(-\tau) \, W_- (x) \, ,\...
- 21
4
votes
3
answers
901
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Wick rotation in Peskin and Schroeder's QFT
I know there are many similar analysis about this topic, like here, here, many of them are answered by Qmechanic, excellent answer!
I have checked most of these posts, but I still don't clearly ...
- 1,421
3
votes
0
answers
153
views
Green Function in Euclidean space time
My question based on Ashok Das's "Finite Temperature Field Theory", page 12-13.
The book assume that in bosonic Klein-Gordon theory, zero temperature Green function satisfies (metric in ...
- 1,421
5
votes
0
answers
163
views
How to obtain imaginary time Green's function from real time Green's function?
Take the following real time time-order Green's function as an example:
\begin{equation}
i G(x, t)=\left\{\begin{array}{l}\frac{1}{\alpha \sqrt{t}} \exp \left[-\beta \frac{x^{2}}{t}\right], t>0 \\ \...
- 1,602
4
votes
0
answers
95
views
Analytic Continuation: Replacement of $t \rightarrow - i \tau$ Mathematical Justification [duplicate]
It's commonly used in imaginary-time path integral that "analytic continuation" means replacing $t \rightarrow - i \tau$ or reparametrizing the theory in terms of imaginary time $\tau = i t$....
- 83
2
votes
2
answers
299
views
Functional derivative for the same function expressed before and after Wick rotation
This question arises when I'm reading section "3.3.1 Minkowski Space" of page 16-17 of the following document: http://www-thphys.physics.ox.ac.uk/people/JohnCardy/qft/qftcomplete.pdf
On page 17, they ...
user148792
5
votes
1
answer
534
views
Wick-rotating the Fourier transform of $\mu+1$ propagators
In Equation (8) of this paper by Groote et. al., we are given the following Euclidean identity:
$$
\int \frac{d^{4}\mathbf{p}_{\mathrm{E}}}{(2\pi)^{4}} \frac{e^{ i \mathbf{p}_{\mathrm{E}} \cdot \...
- 3,719
10
votes
2
answers
1k
views
Euclidean QFT commutator vanishes for all spacetime separations?
In Minkowski spacetime, the commutator of the Klein-Gordon field operator with itself at different spacetime points evaluates to the advanced minus retarded Green's function of the classical theory,
...
- 695
7
votes
1
answer
3k
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Analytic continuation of imaginary time Greens function in the time domain
Consider the imaginary time Greens function of a fermion field $\Psi(x,τ)$ at zero temperature
$$ G^τ = -\langle \theta(τ)\Psi(x,τ)\Psi^\dagger(0,0) - \theta(-τ)\Psi^\dagger(0,0)\Psi(x,τ) \rangle $$
...
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