All Questions
Tagged with quantum-field-theory wick-rotation
156
questions
63
votes
4
answers
6k
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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
45
votes
2
answers
15k
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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
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
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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
19
votes
2
answers
2k
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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
19
votes
1
answer
4k
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Quantum field theory: zero vs. finite temperature
I have recently been made aware of the concept of thermal field theory, in which the introductory statement for its motivation is that "ordinary" quantum field theory (QFT) is formulated at zero ...
- 3,063
18
votes
2
answers
5k
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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:
$$
G_F(x,y) = \lim_{\epsilon \to 0} \frac{1}{(2 \pi)^4} \int d^4p ...
- 910
17
votes
0
answers
1k
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Time Reversal, CPT, spin-statistics, mass gap and chirality of Euclidean fermion field theory
In Minkowski space even-dim (say $d+1$ D) spacetime dimension, we can write fermion-field theory as the Lagrangian:
$$
\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
14
votes
1
answer
1k
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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
13
votes
3
answers
2k
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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
11
votes
3
answers
5k
views
Relation between statistical mechanics and quantum field theory
I was talking with a friend of mine, he is a student of theoretical particle physics, and he told me that lots of his topics have their foundations in statistical mechanics. However I thought that the ...
- 630
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
10
votes
1
answer
225
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Wick Rotation vs Sokhotski-Plemeli Method to compute internal loop of Feynman correlators
When computing loop integrals in QFT, one often encounters integrals of the form
$$\int_{-\infty}^\infty\frac{dp^4}{(2\pi)^4}\frac{-i}{p^2+m^2-i\epsilon},$$ where we are in Minkowski space with metric ...
- 101
10
votes
1
answer
2k
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Path integral and imaginary time in Quantum and Statistical Mechanics
I have come across the path integral formulation of quantum mechanics, and have found plenty of websites, papers and book chapters explaining the relation to statistical mechanics. The general ...
- 101