All Questions
32
questions
2
votes
1
answer
147
views
Derivative interactions in the Wilsonian renormalisation Group
I am currently working through some basic renormalisation group problems, and have come to one about derivative interactions. It has been a while since I have studied QFT formally so bear with me ...
- 90
1
vote
0
answers
49
views
Calculation of Vertex factor from Lagrangian
I am studying spontaneous symmetry breaking of a complex scalar field $\phi(x)$ of a global $U(1)$ symmetry: $\phi(x)\to e^{i\alpha}\phi(x)$, where $\alpha$ is a real constant. I am considering the ...
- 35
2
votes
2
answers
148
views
Derivation of propagator for Proca action in QFT book by A.Zee
Without considering gauge invariance, A.Zee derives Green function of electromagnetic field in his famous book, Quantum Field Theory in Nutshell. In chapter I.5, the Proca action would be,
$$S(A) = \...
- 529
1
vote
0
answers
84
views
Noether charge for dilatations in terms of creation and anihilation operators
I am trying to compute the conserved charge for a continuous diatation symmetry for the massless real scalar field in four dimensions terms of creation and annihilation operators. Then I have,
$$\...
- 368
0
votes
0
answers
49
views
Gaussian integral in condensed matter field
So i need to do the exercise in page 188 from Atland and Simon, "Electron-Phonon copuling". I could do the letter a, the problem is with letter b. I am not sure how to perform the integral ...
- 980
0
votes
0
answers
59
views
How to get The solution of free theory of scalar field with two components?
please consider the following Lagrangian. $$ \mathscr{L}= \int d^4 x \left( \frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi + \frac{1}{2} \partial_{\mu} \psi \partial^{\mu} \psi - V( \phi, \psi) \...
- 1
3
votes
0
answers
50
views
Divergent verticies in mesonic scalar theory [closed]
Considering the following Lagrangian density:
$$ \mathcal{L} = - \frac{1}{2} ( \partial_{\mu} \phi \partial^{\mu} \phi + m^2 \phi^2) + \bar{\psi} (i \gamma^{\mu} \partial_{\mu} - m) \psi + g \bar{\psi}...
- 1,124
2
votes
2
answers
150
views
Does the number of broken generators in SSB depend on the choice of VEV?
I take the Lagrangian,
$$\mathcal{L}=\frac{1}{2}\partial_\mu \phi^T\,\partial^\mu\phi\,-\, \frac{1}{2}\mu^2\phi^T\phi-\frac{\lambda}{4}(\phi^T\phi)^2~,$$
where $\phi=(\phi_1,\,\phi_2,\,\phi_3)$ (real ...
- 35
1
vote
1
answer
161
views
Graviton propagator in Horndeski theory
Let $\phi$ be a scalar field and $g_{\mu \nu} = \eta_{\mu \nu}+h_{\mu \nu}/M_p$ where $M_p$ is the Planck mass (so we assume we deal with perturbations). Let $\Lambda_2,\Lambda_3$ be energy scales ...
- 1,187
1
vote
1
answer
312
views
Feynman rules Horndeski theory
Let $\phi$ be a scalar field and $g_{\mu \nu} = \eta_{\mu \nu}+h_{\mu \nu}/M_p$ where $M_p$ is the Planck mass (so we assume we deal with perturbations). Let $\Lambda_2,\Lambda_3$ be energy scales ...
- 1,187
2
votes
1
answer
283
views
Confused with 4-vector notation and 4-derivative
I have a lot of trouble finding out what the rules are for doing algebra and calculus with 4-vectors. This example shall illustrate one of my problems:
The Lagrangian for a real scalar field is
$$\...
- 1,233
3
votes
0
answers
358
views
Feynman rules of Non-Abelian gauge fields
The Lagrangian of Non-Abelian field is:
\begin{equation}
\mathcal{L} = -\frac{1}{4}[\text{quadratic term} + 2gf^{abc}A_{\mu}^{b}A_{\nu}^{c}(\partial^{\mu}A^{\nu a}-\partial^{\nu}A^{\mu a})+ \text{...
- 145
4
votes
1
answer
257
views
Goldstone theorem in Schwartz
On page 566, Schwartz’s QFT book, to see the $\pi$ is the Goldstone boson, it reads:
$$J^\mu=\frac{\partial L}{\partial(\partial_\mu \pi)} \frac{\delta \pi}{\delta \theta}=F_\pi \partial_\mu \pi \tag{...
- 483
5
votes
1
answer
257
views
Feynman diagrams for $\varphi^3 + \varphi^4$
Given
$$L= -\frac{1}{2}\partial^\mu \varphi \partial_\mu \varphi - \frac{1}{2}m^2\varphi^2 + \frac{\lambda_3}{3!}\varphi^3 - \frac{\lambda_4}{4!}\varphi^4$$
I am trying to find the Feynman diagrams. ...
- 254
1
vote
0
answers
244
views
Most general renormalizable Lagrangian with 2 Weyl spinors and a complex scalar field
I am asked to write down the most general Lorentz-invariant Lagrangian in 4d-spacetime which contains a left-handed Weyl spinor $\psi_{L}$ and a right-handed Weyl-spinor $\psi_{R}$ as well as a ...
- 854