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### 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 ...
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" ...
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-...
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, ...
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 ...
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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 $\left<0\... 0answers 57 views ### Is this the correct way to obtain$<f|i>$term in$\phi^4$interaction theory? [closed] Lets first write the expectation value of the fields in the interaction picture; $$<\Omega|T\phi(x_1)\phi(x_2)\phi(x_1')\phi(x_2')|\Omega>\\=\frac{i\lambda}{4!}<0|T\phi_I(x_1)\phi_I(x_2)\... 1answer 483 views ### What is the leading order Feynman diagram for nucleon-anti-nucleon annihilation into two mesons (\psi^{\dagger} \psi \to \phi\phi)? I am working with a standard basic scalar Yukawa theory. I.e. the only interaction term is -g\psi^\dagger\psi\phi, where the \phi field quanta are the mesons, the \psi field quanta are the ... 1answer 43 views ### How to know what type of diagram contributes to a two-to-two process? There are 3 types of diagrams that can contribute to a two-to-two process; the s-channel, u-channel and t-channel. How do I know what diagrams can contribute to a process? I know that in QED, ... 1answer 926 views ### First-order EM Feynman diagram? Is there any 1st order electromagnetic Feynman diagram? I.e. a process whose probability is just \propto \alpha_{EM}? If not, is there any physical reason why? We always need at least two particles ... 0answers 44 views ### Feynman rules for a general Lagrangian How do I find the Feynman rules for a general Lagrangian density? For example the Lagrangian$$L = \partial_\mu \psi \partial^\mu \psi +a \psi\partial_\mu \psi \partial^\mu \psi+b \psi^2 \partial_\mu ... 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: ... 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 ... 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 ... 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 ... 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 ... 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 $$\int d^dx (\partial^2 \phi^i)\phi_i(\partial_\mu \phi^... 1answer 38 views ### Self-energy in two scalar Yukawa interaction Considering the Lagrangian of two scalar fields in d=4:$$\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$$What would be ... 0answers 60 views ### Properties of Feynman diagrams in Fermi's effective interaction theory What are the properties of the Feynman diagrams in Fermi's effective interaction theory and how can one draw a Feynman diagram in this theory in relation to the Feynman diagram in the standard model ... 0answers 385 views ### Propagator with derivative interaction I work with this interaction Lagrangian density$$\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^... 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 ...