All Questions
9
questions
5
votes
1
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168
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Justification for Wick rotation for topological insulator
In Appendix B of the paper (1), the authors compute the second Chern number $C_2$ of a band structure by manipulating the ground- and excited-state projection operators $P_{\text{G}}(\mathbf{k})$ and $...
- 2,157
6
votes
1
answer
241
views
Validity condition for Wick rotation?
I'm reading page 193 of section 6.3 of the QFT textbook by Peskin and Schroeder. There are two integrals that we need to evaluate for the calculation in this section. (here, $\Delta>0$)
$$\int\frac{...
- 151
2
votes
1
answer
295
views
Why do we Wick rotate before regularizing Feynman diagrams?
In Folland's Quantum Field Theory he mentions that we can apply Feynman's formula (Feynman parameterization) to either the Wick rotated integrals or the non-Wick rotated integrals corresponding to ...
- 3,350
1
vote
1
answer
484
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Why can we do Wick rotations even if $\Delta<0$?
The above page is from Schwartz QFT. Why can we do Wick rotations even if $\Delta<0$?
1
vote
1
answer
313
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Integral and Wick rotation (Srednicki ch75)
I was reading chapter 75 of Srednicki's QFT book and I ran into this statement.
To determine the value of its integral, we
make a Wick rotation to euclidean space, which yields a factor of i as
...
- 35
5
votes
1
answer
534
views
Wick-rotating the Fourier transform of $\mu+1$ propagators
In Equation (8) of this paper by Groote et. al., we are given the following Euclidean identity:
$$
\int \frac{d^{4}\mathbf{p}_{\mathrm{E}}}{(2\pi)^{4}} \frac{e^{ i \mathbf{p}_{\mathrm{E}} \cdot \...
- 3,719
4
votes
1
answer
2k
views
Why doesn't Wick rotation work for this integral?
I thought that for momentum integrals in Minkowski space, the Wick rotation to Euclidean space $k_0 \to ik_0$ allows one to write (let's say $f$ comes with an $i\epsilon$ prescription):
$$\int_{\...
- 2,835
1
vote
0
answers
153
views
Having trouble evaluating a spacetime integral, using Feynman parameterization and wick rotation
I am trying to evaluate the following integral,
$$\int \frac{d^4k}{(2\pi)^2k^2} \left(\frac{\mu}{4M} \right)^2 \frac{k^4 + \frac{1}{3}\vec{k}(k^2 - 2Mk_0)}{(k^4 - 4m^2k_0^2)(k^2 - 2Mk_0)} .$$
My ...
- 145
2
votes
0
answers
2k
views
The Feynman propagator and the $i\epsilon$ prescription
The Feynman propagator is usually represented in the i-epsilon form and texts solve the integral in this form (as opposed to doing the Feynman (time-ordered) contour on the real axis). Restricting ...
- 71