# How do quantum fields really couple?

The term "coupling" between quantum fields refers to certain terms in the Lagrangian (density) $\mathcal{L}$ where the respective field operators appear together, e.g. $g\phi^\dagger\psi$ with coupling constant $g$.

Knowing the mathematical description/origin of a coupling in QFT, I wonder: How can a quantum field $\phi$ of a certain kind excite a quantum state of another totally unrelated type of quantum field $\psi$? Is there are more "physical" picture of how the coupling really happens instead of just a mathematical one?

• I can give you a picture, but not from QFT, rather from simple quantum mechanics. The language in which phenomena are described may differ, but the phenomenon is the same. In the de-excitation of an atom, the movement of the electron is coupled with the states of the electromagnetic field. The coupling constant is given by the interaction law between the movement of a charge and the states of the e.m. field. Feb 10, 2015 at 17:06
• When one quantizes the coupling term $g\phi^\dagger\psi$, one obtains the Feynman diagram vertex. Coupling is represented by vertices in Feynman diagrams. Feb 10, 2015 at 17:26
• "Coupling" isn't special to quantum field theory. In any kind of mechanics, if one thing pushes on another it shows up as a product in the Lagrangian. Feb 10, 2015 at 17:51
• Sure, but when objects in mechanics hit each other, it is due to the same force (mostly electromagnetic repulsion of the constituents). They couple via the same (EM) field. But how can field A excite field B? Maybe there is no satisfying physical picture... Feb 10, 2015 at 17:55
• @quantumorsch likewise in classical mechanics you could ask why do they couple via the EM field. And if you come up with some other kind of "intermediate" interaction you could ask how do they couple to that interaction. The answer to how do they couple is the one you gave: through the interaction term in the Lagrangian. But it seems to me that what you are really looking for is more like why do they do that? See this Phys.SE question about that matter.
– glS
Feb 10, 2015 at 18:15