All Questions
Tagged with quantum-field-theory wick-rotation
32
questions
45
votes
2
answers
15k
views
Wick rotation in field theory - rigorous justification?
What is the rigorous justification of Wick rotation in QFT? I'm aware that it is very useful when calculating loop integrals and one can very easily justify it there. However, I haven't seen a ...
user17116
7
votes
1
answer
2k
views
How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue?
I came across the S. Coleman's seminal papers 'Fate of the false vacuum' (http://dx.doi.org/10.1103/PhysRevD.15.2929, http://dx.doi.org/10.1103/PhysRevD.16.1762) where he describes the tunneling ...
- 3,691
9
votes
1
answer
2k
views
Feynman $i\varepsilon$-prescription in path integral by adding an imaginary part to time
It is known that the well-definiteness of the path integral leads to the Feynman's $i\varepsilon$-prescription for the field propagator. I've found many ways of showing this in the literature, but it ...
63
votes
4
answers
6k
views
How exact is the analogy between statistical mechanics and quantum field theory?
Famously, the path integral of quantum field theory is related to the partition function of statistical mechanics via a Wick rotation and there is therefore a formal analogy between the two. I have a ...
- 3,492
19
votes
2
answers
2k
views
How to understand "analytical continuation" in the context of instantons?
Since this is a subtle and interesting question to me. I will give a rather detailed description. I hope you can keep reading it and find it interesting too.
For simplicity, in the following I will ...
- 3,691
14
votes
1
answer
1k
views
Wick rotation vs. Feynman $i\varepsilon$-prescription
The generating functional $Z[J]$ of some scalar field theory is
\begin{equation}
Z[J(t,\vec{x})]=\int \mathcal{D}\phi e^{i\int (\mathcal{L}+J\phi)d^4x}
\end{equation}
This integral is not well defined ...
- 4,827
4
votes
2
answers
975
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 ...
user148792
25
votes
4
answers
4k
views
What is a simple intuitive way to see the relation between imaginary time (periodic) and temperature relation?
I guess I never had a proper physical intuition on, for example, the "KMS condition". I have an undergraduate student who studies calculation of Hawking temperature using the Euclidean path ...
- 727
21
votes
1
answer
1k
views
LSZ reduction vs adiabatic hypothesis in perturbative calculation of interacting fields
As far as I know, there are two ways of constructing the computational rules in perturbative field theory.
The first one (in Mandl and Shaw's QFT book) is to pretend in and out states as free states, ...
- 6,401
18
votes
2
answers
5k
views
The poles of Feynman propagator in position space
This question maybe related to Feynman Propagator in Position Space through Schwinger Parameter.
The Feynman propagator is defined as:
$$
G_F(x,y) = \lim_{\epsilon \to 0} \frac{1}{(2 \pi)^4} \int d^4p ...
- 910
17
votes
0
answers
1k
views
Time Reversal, CPT, spin-statistics, mass gap and chirality of Euclidean fermion field theory
In Minkowski space even-dim (say $d+1$ D) spacetime dimension, we can write fermion-field theory as the Lagrangian:
$$
\mathcal{L}=\bar{\psi} (i\not \partial-m)\psi+ \bar{\psi} \phi_1 \psi+\bar{\psi} ...
- 7,848
15
votes
2
answers
1k
views
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
13
votes
3
answers
2k
views
Why is Euclidean Time Periodic?
I've been reading a bit about finite temperature quantum field theory, and I keep coming across the claim that when one Euclideanizes time
$$it\to\tau,$$
the time dimension becomes periodic, with ...
- 1,055
6
votes
1
answer
650
views
Two math methods apply the same loop integral lead different results! Why?
I tried to adopt the cut-off regulator to calculate a simple one-loop Feynman diagram in $\phi^4$-theory with two different math tricks. But in the end, I got two different results and was wondering ...
- 91
5
votes
2
answers
482
views
About sending time to infinity in a slightly imaginary direction in QFT
I am going through the Peskin and Schroeder QFT book. While proving the Gell-Mann and Low theorem in chapter 4 of their book, the authors started with the equation
\begin{equation}
e^{-iHT}|0\rangle = ...
- 2,038