Physics — Quantum Field Theory
Routing Summary
Quantum field theory (QFT) and gauge theories: the theoretical machinery underlying the Standard Model. Contains 7 notes. (Consolidated 2026-09-18: the duplicate QFT and gauge-theory overviews from the former
Theoretical Physics/folder were merged into single notes, and its QED and Standard Model notes moved here.)
- Need the conceptual overview of QFT (what it is, why it’s needed, history)? → Quantum Field Theory - Overview
- Need the canonical quantization procedure (ladder operators, Fock space)? → Canonical Quantization of Fields
- Need QED, Feynman diagrams, the Lamb shift and the path integral? → QED and Renormalization
- Need renormalization itself (UV divergences, running couplings, asymptotic freedom)? → Renormalization
- Need gauge symmetry, the Lagrangian, covariant derivatives and fiber bundles? → Gauge Theory - Overview
- Need Yang–Mills theory and non-abelian field strengths? → Yang-Mills Theory and Gauge Fields
- Need the Standard Model gauge structure (QCD, electroweak unification, Higgs)? → Standard Model and Gauge Groups
Concept Map
| Concept | Note | Type | Depends On | Key Result |
|---|---|---|---|---|
| QFT as QM + special relativity + field theory | Quantum Field Theory - Overview | overview | Quantum Mechanics - Overview, Wave Function and Hilbert Space | Fields are operator-valued; particles are excitations; particle number can change |
| Canonical quantization | Canonical Quantization of Fields | concept | Quantum Field Theory - Overview | Klein–Gordon field; creation/annihilation operators |
| QED, Feynman diagrams, renormalization in practice | QED and Renormalization | concept | Quantum Field Theory - Overview, Quantum Mechanics - Mathematical Formalism | Divergences removed by redefining mass/charge; QED accurate to 1 in |
| Renormalization | Renormalization | concept | Canonical Quantization of Fields | Remove UV divergences; running coupling constant |
| Gauge symmetry, local vs global, fiber bundles | Gauge Theory - Overview | overview | Quantum Field Theory - Overview | Local symmetry forces the existence of gauge fields and interactions |
| Yang–Mills theory | Yang-Mills Theory and Gauge Fields | theorem | Gauge Theory - Overview | Non-abelian gauge fields; |
| Standard Model: U(1)×SU(2)×SU(3), gauge bosons | Standard Model and Gauge Groups | concept | Gauge Theory - Overview, QED and Renormalization | All known non-gravitational forces described by gauge theory |
Notes
- Quantum Field Theory - Overview — CONTAINS: motivation, historical development (QED, renormalization, Standard Model), canonical quantization sketch, Dirac equation and antimatter, comparison with QM
- Canonical Quantization of Fields — CONTAINS: scalar field Lagrangian, Klein–Gordon equation, mode expansion, ladder operators, Fock space
- QED and Renormalization — CONTAINS: perturbative infinities, renormalization procedure, Lamb shift, Feynman diagrams, anomalous magnetic moment, path integral formulation
- Renormalization — CONTAINS: UV divergences, renormalization procedure, asymptotic freedom, Lamb shift
- Gauge Theory - Overview — CONTAINS: global vs. local symmetry, gauge fields, Lie groups, covariant derivative, gauge invariance, fiber bundles, gauge bosons
- Yang-Mills Theory and Gauge Fields — CONTAINS: Yang–Mills Lagrangian, field strength tensor, Standard Model gauge group, anomalies
- Standard Model and Gauge Groups — CONTAINS: Yang-Mills theory, QCD, electroweak unification, gauge bosons (photon, W/Z, gluons), Higgs mechanism
Sources
- Quantum field theory — Wikipedia: Quantum field theory (2026-04-10)
- Gauge theory — Wikipedia: Gauge theory (2026-04-10)