All Questions
19
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
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). ...
2
votes
1
answer
143
views
Can you perform a Wick rotation if the poles are on the imaginary axis?
I know you can perform a Wick rotation whenever the poles are outside the contour but what happens if the poles are on the imaginary axis? Can you do it anyway?
- 23
8
votes
2
answers
790
views
Lorentz vs. Euclidean invariance for hard momentum cutoff in QFT
Several accounts of QFT allege that using a hard momentum cutoff $p^2<\Lambda^2$ breaks Lorentz invariance. For instance, see Schwartz's book, p833, or Weinberg p14, or answers here. But I don't ...
- 684
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
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
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 ...
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
4
votes
2
answers
934
views
Wick rotations, convergence and Feynman propagators?
It is said (in e.g. Hawking, 1979, Euclidean quantum gravity) that the integral:
$$ \int \mathcal{D}\phi \exp(iS[\phi])\tag{1} $$
for real fields in Minkowski space does not converge, but the Wick ...
4
votes
1
answer
234
views
Spinor vacuum energy
I'm reading the calculation in the book Quantum field theory in a nutshell of A. Zee of chaoter II.5
In this chapter the vacuum energy is calculated through the path integral approach. At some point ...
- 557
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
8
votes
2
answers
425
views
Why use a particular regularization for $\int_0^\infty \mathrm{d}x\,e^{i p x}$?
There are many badly defined integrals in physics.
I want to discuss one of them which I see very often.
$$\int_0^\infty \mathrm{d}x\,e^{i p x}$$
I have seen this integral in many physical problems. ...
- 467
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