# All Questions

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### Decay and scattering terms in a field theory Lagrangian

Consider two genetic terms in a generic Poincare invariant quantum field theory: A trilinear term of the form $\phi_1\phi_2\phi_3$, and a quartic term of the form $\phi_1\phi_2\phi_3\phi_4$ where ...
300 views

### Feynman diagram of spin Hamiltonian

I am confused about the Feynman diagrams of spin Hamiltonian, for example, the Heisenberg model, the quartic terms like this $$: \begin{align} V &= -\frac{z}{4}\frac{J}{N}\sum_{1,2,3,4}\delta_{...
198 views

### Can all light-matter interactions be reduced to the photoelectric effect, the Compton scattering, and pair production?

My book says that all interaction of light and matter can be reduced to the photoelectric effect, the Compton scattering and pair production. How true is this? What about reflection and absorption ...
587 views

### Propagator Correction in $\phi^4$ theory - why doesn't this secular growth break perturbation theory?

The free propagator for a massive $m\neq0$ real scalar field is the following: $$G_{0}(x,y) \ = \ \int \frac{d^{4}p}{(2\pi)^4} \frac{e^{i p \cdot (x-y)}}{p^2 +m^2 - i \epsilon}$$ It is a well-...
707 views

### Why are derivatives in interaction terms treated differently from derivatives in the kinetic term?

I know that derivative couplings in a Lagrangian interaction, such as $$\mathcal{L}_{int} = \lambda \phi (\partial_{\mu}\phi)(\partial^{\mu}\phi)$$ bring down two momentum factors into the matrix ...
321 views

### How can I see where this formula for a general vertex factor comes from?

I have been reading Srednicki from the beginning and doing all the exercises, and I hit a big roadblock at Q10.4, as I can't seem to figure out what Srednicki is doing in his solution. Luckily, I ...
109 views

### QFT: Range of 'collision'

If two particles approach each other, they can [provided that their properties add to those of other particle(s)] interact and go from, say, $$e + \bar e \to \gamma + \gamma$$ My question is how ...
476 views

### $\phi^{4}$ theory Feynman rules

One of the momentum space Feynman rules in $\phi^{4}$ theory (for correlation functions) is that for an external point with 4-momentum $p$ (with direction headed towards the external point), we need a ...
397 views

### Computing S-Matrix Elements from Feynman Diagrams

In Peskin and Schroeder (PS), the Feynman rules for calculating correlation functions are first presented. Only terms involving all field contractions need to be considered. In Section 4.6, this is ...
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### Creation of momentum on vertex (quantum field theory)

For a an interaction term like $g(\overline{\psi} \gamma^\mu \psi) \partial_\mu \phi$ in which $\psi$ is a Dirac spinor and $\phi$ a scalar field (d=4), should we expect this vertex to have a momentum ...
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### First-order EM Feynman diagram?

Is there any 1st order electromagnetic Feynman diagram? I.e. a process whose probability is just $\propto \alpha_{EM}$? If not, is there any physical reason why? We always need at least two particles ...
4k views

### How to tell the order of a Feynman diagram?

How can we know the order of a Feynman diagram just from the pictorial representation? Is it the number of vertices divided by 2? For example, I know that electnro-positron annihilaiton is first ...
481 views

### What is the leading order Feynman diagram for nucleon-anti-nucleon annihilation into two mesons ($\psi^{\dagger} \psi \to \phi\phi$)?

I am working with a standard basic scalar Yukawa theory. I.e. the only interaction term is $-g\psi^\dagger\psi\phi$, where the $\phi$ field quanta are the mesons, the $\psi$ field quanta are the ...
Consider a theory for a finite number of real scalar fields $\phi _i$ with interaction terms of the form $$-\lambda _{ijk}\phi _i\partial _\mu \phi _j\partial ^\mu \phi _k,$$ with the sum over $i,j,... 1answer 671 views ### Deriving Feynman Rules (with the presence of a gluon field strength tensor) If I have a Lagrangian of the form: $$\mathcal{L} = k \bar{\psi} \varepsilon^{\mu \nu} \lambda^a \phi G^a_{\mu \nu} + h.c.$$ [where$\phi, \psi$are fermions,$\lambda^a$are Gellmann matrices,$\...
I am trying to understand what a term like $$\mathcal{L}_{int} = (\partial^{\mu}A )^2 B^2$$ with $A$ and $B$ being scalar fields for instance means. I understand how to draw an interaction term in ...