All Questions
9
questions
2
votes
0
answers
71
views
Wick rotation of CFT three-point function
Let $\langle O_1\cdots O_n\rangle$ be a Euclidean CFT$_d$ correlation function. I know that we can analytically continue to Lorentzian signature as follows. Let $x_i = (\tau_i,\mathbf{x}_i)\in\mathbb{...
- 36.4k
2
votes
1
answer
303
views
How are Schwinger and Wightman functions used in practice?
In Reed & Simon's Methods of Mathematical Physics Volume II, they define a (Hermitian scalar) quantum field theory to be the quadruple $\langle \mathcal{H}, U, \varphi, D\rangle$ that satisfies ...
- 3,350
1
vote
0
answers
48
views
Why we can Wick rotate momentum axis for correlation function?
In QFT writtern by Peskin and Schroeder, in page 293, PS wick rotate both time axis and momentum axis of correlation function of Klein-Gordon field, ie
$$D_F=<0|T\phi(x_1)\phi(x_2)|0>=\int\frac{...
- 326
2
votes
1
answer
139
views
Do we wick rotate momentum axis on correlation function?
In QFT written by Peskin and Schroeder, it is discussed how correlation function is evaluated in Euclidean space, on page 292 to 293,
In (9.48)
$$<\phi (x_{E1})\phi(x_{E2})>=\int \frac{d^4k_E}{(...
- 326
4
votes
0
answers
123
views
Correlators on the Euclidean section of a black hole
In the standard construction of the Euclidean section of a Schwarzschild black hole, we start with the exterior metric in Schwarzschild coordinates:
$$\tag{1} ds^2 = -(1-r_s/r)dt^2 + (1-r_s/r)^{-1}dr^...
- 1,455
2
votes
0
answers
145
views
How to analytically continue Schwinger functions?
To get Wightman functions $W(t_1, \dots, t_{k-1})$ from Schwinger functions $S(\tau_1 = i t_1, \dots)$, we use analytical continuation.
But I don't think this is simply an issue of plugging $it_a$ for ...
- 16.2k
2
votes
1
answer
603
views
What is the link between statistical and QFT correlation functions?
I'm studying statistical mechanics in particular correlation function:
https://en.wikipedia.org/wiki/Correlation_function_(statistical_mechanics)
and I have understood it. Now searching on internet ...
- 444
9
votes
1
answer
874
views
Is there any physical meaning for such a correlation function?
Consider a thermal scalar field theory, we have the partition functional
$$Z={\rm tr}(e^{-\beta H}).$$
We can build this theory as an Euclidean quantum field theory
$$Z=\int\mathcal{D}\Phi\,e^{-S_E[\...
- 3,691
5
votes
2
answers
1k
views
Transition amplitudes by functional methods in QFT
I am following section 9.2 in Peskin and Schroeder in which the Feynman rules are derived for scalar fields.
They define (in eqn (9.14), page 282) the transition amplitude from $\vert\phi_a\rangle$ ...
- 211