All Questions
9
questions
10
votes
1
answer
225
views
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
0
votes
1
answer
154
views
Calculation of one-loop diagram in $\phi^4$ theory
In Folland's book Quantum Field Theory, page 207, he gives the value of the amputated one-loop $\phi^4$ diagram as
$$I(p) = \frac{(-i\lambda)^2}{2} \int \frac{-i}{-q^2 + m^2 - i\epsilon} \cdot \frac{-...
- 3,350
2
votes
1
answer
295
views
Why do we Wick rotate before regularizing Feynman diagrams?
In Folland's Quantum Field Theory he mentions that we can apply Feynman's formula (Feynman parameterization) to either the Wick rotated integrals or the non-Wick rotated integrals corresponding to ...
- 3,350
4
votes
1
answer
448
views
Peskin and Schroeder Page no. 95 Feynman Diagrams
From Peskin and Schroeder Page no. 95,
... First, what happened to the large time $T$ that was taken to $\infty(1- i\epsilon)$? We glossed overit completely in this section, starting with Eq. (4.43). ...
1
vote
2
answers
757
views
The way momentum space integrals tend to infinity
At the beginning of chapter 15 of Schwartz, he states that
$$\int d^4k \frac{k^2}{k^4}=\int \frac{d^4k}{k^2}\sim \int k\ dk. $$
I don't see how he got this at all. Isn't this just the integral
\...
- 4,780
4
votes
0
answers
491
views
Is Wick rotation of loop integrals legitimate?
In Feynman diagram calculations, we seem to invariably Euclideanise loop integrals in order to exploit the resulting spherical symmetry. This Wick rotation is simply a deformation of the contour; ...
- 6,425
2
votes
1
answer
690
views
Schroeder's Minkowski Space Integral - Concerns about Wick Rotations
In the Appendix of Peskin & Schroeder's "An Introduction to Quantum Field Theory" there is a list of integrals in Minkowski space. Of particular interest to me is the integral (A.44):
$$
I(\Delta) ...
- 3,719
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
4
votes
1
answer
1k
views
Wick Rotation, interpretation of $\bar{p}^2$ vs the usual $p^2=m^2$
Suppose we use the metric $(+,-,-,-)$ thus the momentum squared is
$p^2 = p_0^2-\vec{p}^2 = m^2>0$
Defining $p_E:=\mathrm{i}\cdot p_0$ and $\bar{p}:=(\,p_E,\vec{p})$ with Euclidean norm $\bar{p}...
- 101