Specific Quantum Field Theories

Notes on concrete instances of quantum field theory. The general formalism (postulates, definitions, foundational issues) is collected in the parent QFT folder; this subfolder covers specific theories obtained by choosing field content, symmetries, and a renormalizable Lagrangian.

Contents

• Quantum Electrodynamics (QED) — the $U(1)$ gauge theory of electrons, positrons, and photons (modern gauge-principle derivation).
  • Historical (Dirac-Equation) Route — the same theory built up the textbook way: Dirac equation, minimal coupling, second quantization.
  • Compton Scattering — the easiest real QED calculation: tree-level $e\gamma \to e\gamma$, closed-form Klein–Nishina cross section.
  • The Hydrogen Atom in QED — worked example showing how Schrödinger, Dirac fine structure, the Lamb shift, and hyperfine splitting arise as successive approximations in $\alpha$ and $m_e/m_p$.
• Quantum Chromodynamics (QCD) — the $SU(3{)}_{\text{color}}$ gauge theory of quarks and gluons; structurally parallel to QED but qualitatively different in dynamics (asymptotic freedom, confinement, ghost-dependence, gluon self-coupling).
• Electroweak Theory — the $SU(2{)}_L\times U(1{)}_Y$ gauge theory unifying QED with the weak interaction, spontaneously broken to $U(1{)}_{\text{EM}}$ by the Higgs mechanism. Introduces chiral fermions, massive gauge bosons ($W^{\pm },Z^0$), the Higgs boson, and CKM mixing.
• The Standard Model — the union $SU(3{)}_C\times SU(2{)}_L\times U(1{)}_Y$ of QCD and electroweak, with the cross-sector content (anomaly cancellation, generations + GIM, two CP problems, accidental symmetries) that only makes sense once both are combined.