All Questions
126
questions
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23
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Possible decays of a scalar particle, Feynman diagrams and calculation of branching ratio - Explenation of solution required
Consider the Lagrangian describing two Dirac fields of masses $m_1$ and $m_2$ and a scalar neutral field of mass $M$, which in addition to the free terms contains the following interaction term
\begin{...
- 17
3
votes
1
answer
92
views
How can I count diagrams (in this scalar QED example) at a particular order without drawing all the Feynman diagrams?
Here's a 3-loop diagram for light-by-light scattering in scalar QED (from Schwartz textbook question 9.2):
The question 9.2 asks approximately how many other diagrams contribute at the same order in ...
- 1,783
6
votes
0
answers
99
views
Fourier transform of Feynman Integral
In Nastase, Introduction to AdS/CFT, the first chapter talks a little about the star-triangle duality. In fact, it was claimed that the Fourier Transform of a Feynman-like diagram in position space in ...
- 980
1
vote
0
answers
59
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Peskin and Schroeder page 201, solving integral over angular part
They make the following steps:
$$\int\frac{\Omega_\bf{k}}{4\pi}\ \frac{1}{(\hat{k}\cdot p')(\hat{k}\cdot p)} = \int_0^1d\xi\int\frac{\Omega_\bf{k}}{4\pi}\frac{1}{(\xi\ \hat{k}\cdot p'+(1-\xi)\ \hat{k}\...
- 327
1
vote
1
answer
73
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Peskin and Schröeder page 195, IR divergence in the electron vertex function, rewriting integral
Peskin and Schröeder make the following statement
$$\int_0^1dxdydz\ \delta(x+y+z-1)\frac{1-4z+z^2}{\Delta(q^2=0)}=\int_0^1dz\int_0^{1-z}dy\frac{-2+(1-z)(3-z)}{m^2(1-z)^2},\tag{p.195}$$
where $$\Delta =...
- 327
1
vote
1
answer
71
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Trouble Understanding Computation In Nucleon Scattering Example in David Tong Lecture Notes
I am struggling to understand the following computation from page 59 of Tong's QFT notes
http://www.damtp.cam.ac.uk/user/tong/qft.html
The expression
$$
(-ig)^{2} \int \frac{d^{4}k}{(2\pi)^{4}} \frac{...
- 23
-1
votes
1
answer
130
views
Massless Sunset Diagram $\phi^4$ [closed]
I should compute an explicit calculation for the sunset diagram in massless $\phi^4$ theory.
The integral is $$-\lambda^2 \frac{1}{6} (\mu)^{2(4-d)}\int \frac{d^dk_1}{(2\pi)^d} \int \frac{d^dk_2}{(2\...
- 7
1
vote
0
answers
60
views
Feynman parameters for $n=3$
I proved the general formula for the Feynman parameters:
\begin{equation}
\frac{1}{P_1^{a_1}...P_n^{a_n}}=\frac{\Gamma(a_1+...+a_n)}{\Gamma(a_1)...\Gamma(a_n)}\int_0^1dx_1...dx_n\delta(1-x_1-...-x_n)\...
- 357
2
votes
1
answer
146
views
2-loop correction to exact 3-point vertex in a complex scalar field theory with cubed interaction
I am a graduate student with 1 quarter of relativistic QFT at the level of Srednicki (covered up to Chapter 30 this Fall). This question is not in any book that I know off and it wasn't assigned as ...
- 1,713
1
vote
0
answers
52
views
External leg correction to 3-point QED Green's function
I am trying to calculate the following diagram to solve the Callan-Symanzik equation for the three-point Green's function (two massless fermions and a photon).
The counterterm to the photon ...
- 1,075
3
votes
0
answers
76
views
Getting equation (16.159) in Ashok Das' QFT textbook
I am having difficulty in getting equation (16.159), page 730, in the book "Lectures on Quantum Field Theory", 1st edition, by Ashok Das. (The equation and page number is slightly different ...
- 513
-1
votes
1
answer
74
views
Performing Feynman parameter integral [closed]
How can I evaluate this integral?$$\int_0^1\int_0^1\int_0^1\frac{z}{1-z}\delta(x+y+z-1)dxdydz$$ I am getting $2\ln2-1$, but the answer should be $\frac12$.
0
votes
1
answer
72
views
Odd number of momentum should vanish but doesn't? [closed]
I have the following integral found within a loop-calculation (the actual content of the Feyman diagram, this is purely a math question)
\begin{equation}
J_\mu = \int\frac{d^4l}{(2\pi)^4}\frac{l_\mu}{...
- 704
2
votes
1
answer
198
views
Symmetry Factor and Wicks Theorem
I have a problem with a particular kind of exercise. The question is:
Consider $\phi^4$-theory with $\mathcal{L}_\text{int}=-\frac{\lambda}{4!}\phi^4$. Give the symmetry factors of the diagram and ...
- 23
1
vote
0
answers
102
views
Yukawa theory: Fermion-Antifermion scattering
I have the following Yukawa theory: $$\mathcal{L} =\frac{1}{2}\partial_{\mu}\phi \partial^{\mu} \phi-\frac{1}{2}M\phi^2+\bar\psi(i\gamma^{\mu}\partial_{\mu}-m)\psi-g\bar{\psi}\psi\phi$$
and a fermion-...
- 15