All Questions
23
questions
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0
answers
31
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Lorentz transformation of Creation and Annihilation operators for a real scalar field theory - MIT OCW QFT I Problem set 3 [closed]
I have been working through the MIT OCW's QFT lecture notes and problem sets, but I have come to realize that I have a fundamental misunderstanding of what is meant by how objects transform under ...
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
0
votes
0
answers
142
views
Does Furry's Theorem for QED hold in lower dimensions as well?
In $1+3$ dimensional QED, it is well-known that an amplitude for a process described by a Feynman diagram with odd number of vertices is zero.
This is Furry's Theorem.
I wonder if this theorem holds ...
- 1,669
3
votes
2
answers
289
views
How to prove a single-point correlation function equal to zero?
A short question, when I am studying QFT-P&S's book, try to use completeness relation (7.2) to expand the two-point correlation function: $$\langle\Omega|\hat T{\phi(x)\phi(y)}|\Omega\rangle\tag{7....
1
vote
1
answer
896
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Third-order Feynman diagrams of 2-point function in $\phi^4$-theory [closed]
$\newcommand{\Braket}[1]{\left<\Omega|#1|\Omega\right>}$
Hello,
I am currently studying QFT and have a problem concerning the 2-point correlation function in $\phi^4$-theory. When I draw all the ...
- 157
4
votes
0
answers
486
views
Symmetry factors for feynman diagrams from complex scalar interaction term
My question regards a quantum field theory with an interaction term $${\mathcal{L_{int}}=-\frac{\lambda}{4}\phi^\dagger}^2 \phi^2.$$ It's claimed in the solutions to a problem sheet that the one-loop ...
- 167
2
votes
0
answers
459
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Computing symmetry/combinatorial factor for a diagram in $\phi^4$ theory
I am working with $\lambda\phi^4/4!$ theory and am struggling to compute the symmetry factor for the diagram
by using the method specified here. I know that the answer is ${1}/{12}$, but I can't work ...
- 2,157
1
vote
0
answers
157
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Time reversal symmetry of scalar field theory
Can anyone prove the time-reversal invariance of the following scalar field theory?
$$ \mathcal{L}=\frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi-\frac{\mu^{2}}{2} \phi^{2}-g\phi\psi^*\psi+\...
- 369
2
votes
1
answer
195
views
Getting wrong number of Wick contractions
Consider this lagrangian:
$$\mathcal{L} = \dfrac{1}{2} (\partial_{\mu}\phi_{1})^2 + \dfrac{1}{2} (\partial_{\mu}\phi_{2})^2 + \dfrac{m^2}{2}(\phi_{1}^2 + \phi_{2}^2) + \dfrac{g}{4!}(\phi_{1}^4 + \phi_{...
- 513
2
votes
2
answers
1k
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Symmetry factor of certain 1-loop diagrams in $\phi^4$-theory
I have to derive a formula for the symmetry factor of the diagrams of the form
in $\phi^4$-theory, where $\phi$ is a real scalar field. By symmetry factor I mean only the number of possible ...
- 854
1
vote
0
answers
97
views
Stability and global symmetries of complex scalar field theory [closed]
Given the Lagrangian of a complex scalar field:
$$ \mathcal L = \partial_{\mu} \phi^* \partial^{\mu} \phi - m^2 \phi^* \phi - \frac 12 \mu^{4-2n} \phi^{2n} - \frac 12 (\mu^*)^{4-2n} (\phi^*)^{2n} \, ,$...
- 186
2
votes
1
answer
1k
views
Calculating the symmetry factor of the sunset Feynman diagram
Edit: This is in $\phi^4$ theory.
Given this Feynman diagram
And using this formula to calculate the symmetry factor
$S = v\prod_{k}(k!)^{\pi _{k}}$
I calculate: $v = 1$, as you can only change ...
1
vote
1
answer
179
views
How to obtain the Noether charge for two interacting fields. Correct mode expansion for field operators
If I have two interacting fields
$$
\mathcal{L} = \frac{1}{2}(\partial_\mu \phi_1)^2 - \frac{1}{2}m^2\phi_2^2
+ \frac{1}{2}(\partial_\mu \phi_2)^2 - \frac{1}{2}m^2\phi_2^2 - g^2(\phi_1^2 + \phi_2^2)^...
- 793
1
vote
1
answer
704
views
How to show that the charge conjugation reverses the charge of a state?
How to show that the charge conjugation operator reverses the charge(s) of a (fermionic or bosonic) state?
Let us consider a spin-$\frac{1}{2}$ fermionic state of momentum $\textbf{k}$ and spin ...
- 26.8k
3
votes
1
answer
2k
views
Transformation of field operator under $SU(2) \times SU(2)$
I am a little confused on how field operators transform under compound symmetry groups. The following text is copied from Michael Dine Supersymmetry and String Theory
As an example, relevant both to ...
- 961