From Quantum Field Theory to Cavity Quantum Electrodynamics [Higher and More Subtle Electrodynamics · 6]

hfwang132@gmail.com (hfwang132) — Sun, 13 Apr 2025 01:52:37 +0800

In this article, we start from the QED Lagrangian:

\[\begin{aligned} \mathcal{L}= \bar{\psi}(\mathrm{i}\gamma^\mu \partial_\mu -m)\psi - eA_\mu \bar{\psi} \gamma^\mu \psi -\frac{1}{4} F_{\mu\nu} F^{\mu\nu} \end{aligned} \]

This Lagrangian is highly complex: it not only takes into account the electron’s antiparticle—the positron—but the coupling term \(- eA_\mu \bar{\psi} \gamma^\mu \psi\) is also a cubic term, capable of describing various processes such as electron-positron pair creation/annihilation. Due to the presence of the cubic term, this Lagrangian has no analytic solution and can only be solved using perturbation theory in quantum field theory.

Jaynes-Cummings on Haifei's Home

From Quantum Field Theory to Cavity Quantum Electrodynamics [Higher and More Subtle Electrodynamics · 6]