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21
votes
1answer
6k views

Interpretation of derivative interaction term in QFT

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 ...
9
votes
1answer
4k views

How can the Feynman rules be read off the Lagrangian?

I am reading Peskin. In his functional methods chapter he says that (i) "Once the quadratic terms in the Lagrangian are properly understood" and (ii) "The propagators of the theory are computed" ...
7
votes
2answers
596 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-...
6
votes
2answers
1k views

Feynman diagram for attractive forces

I’m looking at Feynman diagrams for attractive forces and I'm thoroughly confused. Below are three diagrams from HyperPhysics: These all illustrate instances where the forces are attractive. However, ...
5
votes
2answers
715 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 ...
5
votes
1answer
257 views

Feynman diagram representation of variational derivative of S-matrix

For quite some time I am struggling to understand section 6.4 in Weinberg volume 1. He observes there that if interaction hamiltonian density is extended by coupling to c-number fields $\epsilon$, $$ \...
5
votes
1answer
64 views

Feynman diagrams as topology

When we talk about Feynman diagrams we know they are tools to make calculations easier and more intuitive. Moreover, it's said that they are "topological" representations of the interactions. But, ...
4
votes
1answer
674 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, $\...
4
votes
1answer
348 views

Feynman rules out of the Lagrangian

Accordingly to chapter 10, section 10.6 Feynman Rules of 'Introduction to Elementary Particles' by David Griffiths, there is a way to extract the vertex and propagators just by inspection of the ...
4
votes
1answer
554 views

Feynman rule for deriative interaction: an example

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,...
4
votes
1answer
311 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 $[1]$: \begin{align} V &= -\frac{z}{4}\frac{J}{N}\sum_{1,2,3,4}\delta_{...
4
votes
0answers
330 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 ...
2
votes
2answers
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 ...
2
votes
1answer
225 views

What happens in the Hartree and Fock diagrams?

I am trying to understand the Hartree and Fock diagram shown in the picture. To understand it a assume there is an electron entering and leaving at the tail of the tadpole (Hartree diagram) and an ...
2
votes
1answer
411 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 ...
2
votes
2answers
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 ...
2
votes
1answer
351 views

Photon propagator counterterm in QED

The lagrangian for QED including counterterms is $$\mathcal{L} = -\frac{1}{4}F_{\mu \nu}^{2}+i\bar{\psi}\gamma^{\mu}{\partial_{\mu}} \psi-m_R \bar{\psi}\psi-e_R \bar{\psi}\gamma^{\mu}A_{\mu}\psi- \...
2
votes
0answers
71 views

Feynman Rules from Lagrangian with charge conjugation matrix

I'm dealing with a doubly charged scalar singlet that interacts only with the right-handed muon as follows, $$\mathcal{L} = \lambda \psi_{R}C\psi_{R} \phi^{++},$$ where $\lambda$ is the coupling, $\...
2
votes
0answers
97 views

Feynman rules for anomalous vertex [closed]

We can read Feynman rules directly from the lagrangian in the simplest cases, but for the following lagrangian I am a few stuck $\mathcal{L}=4g\phi\epsilon^{\mu\nu\rho\sigma}\partial_{\mu}A_{\nu}\...
2
votes
0answers
272 views

Question about interacting fields and feynman diagrams [closed]

The picture is taken from Chapter 4: 'Interacting Fields and Feynman Diagrams in An Introduction to Quantum Field Theory by Peskin and Schroeder. There is a two point correlation function $\left<0\...
2
votes
0answers
57 views

Is this the correct way to obtain $<f|i>$ term in $\phi^4$ interaction theory? [closed]

Lets first write the expectation value of the fields in the interaction picture; $$ <\Omega|T\phi(x_1)\phi(x_2)\phi(x_1')\phi(x_2')|\Omega>\\=\frac{i\lambda}{4!}<0|T\phi_I(x_1)\phi_I(x_2)\...
1
vote
1answer
483 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 ...
1
vote
1answer
43 views

How to know what type of diagram contributes to a two-to-two process?

There are 3 types of diagrams that can contribute to a two-to-two process; the $s$-channel, $u$-channel and $t$-channel. How do I know what diagrams can contribute to a process? I know that in QED, ...
1
vote
1answer
926 views

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 ...
1
vote
0answers
44 views

Feynman rules for a general Lagrangian

How do I find the Feynman rules for a general Lagrangian density? For example the Lagrangian $$L = \partial_\mu \psi \partial^\mu \psi +a \psi\partial_\mu \psi \partial^\mu \psi+b \psi^2 \partial_\mu ...
1
vote
0answers
150 views

Why isn't energy conserved in time-ordered diagrams?

I'm new to particle physics, and I'm reading chapter 5 of Prof. Mark A. Thompson's "Modern Particle Physics", which talks about Time-ordered perturbation theory vs QED. However, in page 119 he wrote: ...
1
vote
0answers
483 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 ...
1
vote
0answers
91 views

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 ...
0
votes
2answers
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 ...
0
votes
1answer
72 views

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 ...
0
votes
0answers
39 views

Feynman rules for scalar field with second order derivatives in the interaction term

Given the interaction term with $N$ scalars $\phi_i$, each massless, what would be the Feynman rules for an interaction term in the action as $$ \int d^dx (\partial^2 \phi^i)\phi_i(\partial_\mu \phi^...
0
votes
1answer
38 views

Self-energy in two scalar Yukawa interaction

Considering the Lagrangian of two scalar fields in $d=4$: $$\mathcal{L}=\frac{1}{2}(\partial\phi)^2-\frac{1}{2}m^2\phi^2+\frac{1}{2}(\partial\chi)^2-\frac{1}{2}M^2\chi^2-g\phi^2\chi$$ What would be ...
0
votes
0answers
60 views

Properties of Feynman diagrams in Fermi's effective interaction theory

What are the properties of the Feynman diagrams in Fermi's effective interaction theory and how can one draw a Feynman diagram in this theory in relation to the Feynman diagram in the standard model ...
0
votes
0answers
385 views

Propagator with derivative interaction

I work with this interaction Lagrangian density $$\mathcal{L}_{int} = \mathcal{L}_{int}^{(1)} + \mathcal{L}_{int}^{(2)} + {\mathcal{L}_{int}^{(2)}}^\dagger = ia\bar{\Psi}\gamma^\mu\Psi Z_\mu +ib(\phi^...
-3
votes
2answers
94 views

Why can't two real photon, gluon, graviton, and $W$ and $Z$ fields interact by means of their virtual counterparts (the mediators of the process)?

It is a fact that two real (massless) photons, gluons, or gravitons can't react by means of their virtual counterparts (for example, two external photons that interact via one of these massless ...