Photons: Quantizing the Electromagnetic Field
A full lecture reconstruction showing how the free electromagnetic field in Coulomb gauge becomes an infinite set of quantum harmonic oscillators whose quanta are photons, and why gauge-invariant observables still preserve relativistic causality in photon detection.
Introduction
This lecture is where the electromagnetic field finally becomes a genuine quantum field in the same concrete way that the scalar and Dirac fields did earlier in the course.
Up to now, the Maxwell field has been brought into Hamiltonian form in Coulomb gauge. That already gave a clear classical picture: - two transverse dynamical degrees of freedom, - transverse electric and magnetic radiation fields, - plus the instantaneous Coulomb electric field tied directly to the charge density.
But that was still classical field theory.
A full lecture reconstruction showing how the gauge-invariant Maxwell–Dirac Lagrangian leads, after constraints and gauge fixing, to the Hamiltonian formulation of electrodynamics in Coulomb gauge, with only the two transverse dynamical photon degrees of freedom remaining.
A full lecture reconstruction introducing perturbative quantum electrodynamics from the Coulomb-gauge Hamiltonian, identifying the fine-structure constant as the small expansion parameter, and using time-independent perturbation theory to analyze the QED vacuum and one-electron states.