All Questions
Tagged with quantum-field-theory wick-rotation
156
questions
2
votes
2
answers
1k
views
Why do people use real values for the Wick-rotated time $\tau$?
In doing instanton problems or when connecting quantum field theory to statistical mechanics, I often see people trying the Wick rotation trick by defining an imaginary time $\tau\equiv it$. So, in ...
- 195
0
votes
1
answer
286
views
Does Wick rotation work for time-dependent Hamiltonian?
Consider a quantum system that is governed by a Hamiltonian with explicit time dependence $H(t)$.
Is it always legitimate to perform a Wick rotation $t \rightarrow -i\tau$, and calculate the time-...
- 1
2
votes
1
answer
319
views
What's wrong with using a vielbein to define Wick rotation?
Wick rotation is supposed to be a relationship between field theories with spacetime metrics of Lorentzian and Euclidean signature. I thought the definition of Wick rotation was settled, until I came ...
- 54.5k
6
votes
1
answer
171
views
Besides dim regularization, what are the advantages of Euclidean QFT?
Initially, I saw Wick rotation as a useful trick to apply dimensional regularization, but then I learned about instantons and how they only exist in Euclidean Yang-Mills.
Also, I heard that path ...
- 125
0
votes
1
answer
37
views
Why does this distribution function depend on time and not temperature?
When reading Sterile neutrino hot, warm, and cold dark matter I came across the following momentum distribution function for a neutrino species $\alpha$:
$$\tag{5.8} f(p,t) = \frac{1}{e^{E(p)/T + \...
- 753
5
votes
2
answers
482
views
About sending time to infinity in a slightly imaginary direction in QFT
I am going through the Peskin and Schroeder QFT book. While proving the Gell-Mann and Low theorem in chapter 4 of their book, the authors started with the equation
\begin{equation}
e^{-iHT}|0\rangle = ...
- 2,038
3
votes
1
answer
280
views
Is there any difference between signature $(1,1)$ and $(2,0)$ in 2D CFT?
Is there any difference between signature $(1,1)$ and $(2,0)$ in 2D CFT?
The only thing I could thought of was that the previous one had Lorentz symmetry and the later one was Euclidean (rotation), ...
- 3,256
5
votes
2
answers
533
views
What does the Temperature of a QFT physically mean?
In elementary statistical mechanics, one can think of temperature as arising from the average kinetic energy of particles in the ensemble. Is there a similar way to think about the temperature of a ...
- 1,055
13
votes
3
answers
2k
views
Why is Euclidean Time Periodic?
I've been reading a bit about finite temperature quantum field theory, and I keep coming across the claim that when one Euclideanizes time
$$it\to\tau,$$
the time dimension becomes periodic, with ...
- 1,055
1
vote
0
answers
256
views
What is the entropy and/or equation of state of a partition function such as $Z=\int D\phi \exp (i S[\phi]/\hbar)$?
At this link https://en.wikipedia.org/wiki/Partition_function_(mathematics), it is claimed that the following partition function:
$$
Z=\int D\phi \exp (-\beta H[\phi]) \tag{1}
$$
is a consequence of ...
- 1,548
6
votes
1
answer
616
views
Proving that a Wick rotation is valid for a quantum field theory
While trying to find out if there is a rigorous justification for Wick rotating a QFT, I came across this other question (link below [1]) that mentions the Osterwalder-Schrader Theorem that gives a ...
- 733
2
votes
1
answer
2k
views
Scalar field propagator in euclidean field theory
We have a scalar field propagator in minkowski space with signature $(+,-,-,-)$ as
$$ G (k)={1\over
k^2-m^2 }.$$
But in Euclidean space the scalar field propagator is
$$G (k)={1\over k^2+m^2 }.$$
...
- 545
4
votes
2
answers
681
views
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
7
votes
1
answer
206
views
Choice of folliation in path integral
Assume we have a scalar field theory for a field $\phi$. Can we think of the Hilbert space as being spanned by states of the form $|\varphi\rangle$ for configurations $\varphi\in C^\infty(\mathbb{R}^3)...
- 3,915
5
votes
1
answer
874
views
Convert propagators from Euclidean to Minkowski spacetime
I'm looking for a rule to "convert" the propagators of a quantum field theory formulated in Euclidean spacetime into those of the same theory but in Minkowski spacetime (with the $\operatorname{diag}(-...
- 660