Quantum Electrodynamics (QED) is the quantum field theory that describes how light and matter interact. It is the most precisely tested theory in all of science — its predictions match experiment to better than one part in a trillion. Understanding QED means understanding the fundamental nature of electricity, magnetism, and light at the deepest level we currently know.
The Central Idea: Fields and Their Quanta
In QED, the electromagnetic field is not a classical smooth field but a quantum field — an operator-valued function of spacetime that can be in superpositions of different configurations. Excitations of this field are photons. Similarly, the electron field's excitations are electrons (and their antimatter partners, positrons).
Every interaction in QED comes down to a single primitive vertex: an electron emits or absorbs a photon. All of electromagnetism — attraction between opposite charges, repulsion between like charges, the photoelectric effect, Compton scattering — emerges from combinations of this one fundamental act.
Feynman Diagrams
Richard Feynman invented a pictorial language for systematically calculating interaction probabilities. Each diagram represents a term in a perturbation series expansion:
- Straight lines with arrows represent electrons (arrow forward = electron, arrow backward = positron)
- Wavy lines represent photons
- Each vertex where these lines meet contributes a factor proportional to the electron charge
e
The simplest process — two electrons repelling each other — is drawn as two electron lines exchanging a single photon. This photon is virtual: it exists only as an intermediate state and is not directly observable. Virtual particles are permitted to violate the ordinary energy-momentum relation E^2 = (pc)^2 + (mc^2)^2 because of the time-energy uncertainty principle.
Higher-order corrections add more vertices and loops. A one-loop correction to electron scattering involves the exchanged photon briefly splitting into a virtual electron-positron pair. Each additional loop multiplies the contribution by a factor of the fine structure constant:
alpha = e^2 / (4*pi*eps_0*hbar*c) ≈ 1/137.036
Since alpha is small, higher-order corrections get progressively smaller, making the perturbation series converge rapidly and accurately.
The Fine Structure Constant
alpha is the most important dimensionless number in QED. It sets the strength of the electromagnetic coupling — roughly speaking, the probability amplitude for an electron to emit a photon is proportional to sqrt(alpha).
The mystery of why alpha ≈ 1/137 has no answer within current physics. Feynman described it as "one of the greatest mysteries of physics" and noted that if its value differed by even a few percent, atoms as we know them could not exist. It sits at the boundary between the computable and the unexplained.
The Path Integral Formulation
Feynman's path integral approach provides the deepest intuition for quantum mechanics. Rather than a particle traveling a single definite trajectory, every possible path through spacetime contributes to the final probability amplitude. Each path is weighted by:
exp(i*S/hbar)
where S is the classical action (integral of the Lagrangian) along that path. Paths near the classical trajectory interfere constructively because neighboring paths have nearly the same phase. Paths far from the classical trajectory interfere destructively and cancel. As hbar approaches zero, only the classical path survives — this is how quantum mechanics recovers classical mechanics in the limit.
In QED, the Lagrangian that enters this path integral is:
L = psi-bar*(i*gamma^mu*D_mu - m)*psi - (1/4)*F_mu_nu*F^mu_nu
The first term describes free electrons (with minimal coupling to the electromagnetic field through the covariant derivative D_mu). The second term is the kinetic energy of the electromagnetic field itself, expressed through the field strength tensor F.
Renormalization: Taming the Infinities
QED's perturbation series produces apparent infinities. Loop diagrams involve integrals over all possible momenta of the virtual particles, and these integrals diverge at high momenta. For decades this seemed to make the theory meaningless.
The resolution is renormalization. The key insight is that what we call the electron's mass and charge are not the bare parameters in the Lagrangian — they include all quantum corrections. We can absorb the infinities into the definition of these physical parameters. The theory makes finite, unambiguous predictions for differences between measurable quantities.
This procedure, developed by Julian Schwinger, Sin-Itiro Tomonaga, and Richard Feynman (and made mathematically rigorous by Freeman Dyson), is not a trick — it reflects the deep physics that all measurements are relative, and that separating bare quantities from their fluctuation corrections is always a matter of scale.
The Anomalous Magnetic Moment
The most famous test of QED is the anomalous magnetic moment of the electron, denoted g - 2. Classical theory predicts g = 2. QED predicts corrections from virtual photon loops:
Theory: g/2 = 1.001 159 652 181 78 (± 0.00000000000077)
Experiment: g/2 = 1.001 159 652 180 59 (± 0.00000000000013)
Agreement to 12 significant figures. No other theory in the history of physics has achieved this level of precision. QED is not merely correct — it is extraordinarily, almost unreasonably, correct. It is the gold standard against which all other physical theories are judged.