Physics — Quantum Field Theory
Routing Summary
Quantum field theory (QFT) and gauge theories: the theoretical machinery underlying the Standard Model.
- Need the conceptual overview of QFT (what it is, why it’s needed)? → QFT Overview
- Need the canonical quantization procedure (ladder operators, Fock space)? → Canonical Quantization of Fields
- Need renormalization and how infinities are removed? → Renormalization
- Need gauge symmetry, the Lagrangian, and covariant derivatives? → Gauge Theory Overview
- Need Yang–Mills theory and the Standard Model gauge group? → Yang-Mills Theory and Gauge Fields
Concept Map
| Concept | Note | Type | Depends On | Key Result |
|---|---|---|---|---|
| QFT overview | QFT Overview | overview | QM | Fields are operator-valued; particles = excitations |
| Canonical quantization | Canonical Quantization of Fields | concept | QFT Overview | Klein–Gordon field; creation/annihilation operators |
| Renormalization | Renormalization | concept | Canonical Quantization | Remove UV divergences; running coupling constant |
| Gauge theory | Gauge Theory Overview | overview | QFT Overview | Local symmetry mandates gauge field; gauge boson |
| Yang–Mills theory | Yang-Mills Theory and Gauge Fields | theorem | Gauge Theory | Non-abelian gauge fields; Standard Model |
Notes
- QFT Overview — COVERS: motivation, history (QED, renormalization, Standard Model), comparison with QM
- Canonical Quantization of Fields — COVERS: scalar field Lagrangian, Klein–Gordon equation, mode expansion, ladder operators, Fock space
- Renormalization — COVERS: UV divergences, renormalization procedure, asymptotic freedom, Lamb shift
- Gauge Theory Overview — COVERS: global vs. local symmetry, fiber bundles, gauge field, covariant derivative, gauge boson
- Yang-Mills Theory and Gauge Fields — COVERS: Yang–Mills Lagrangian, field strength tensor, Standard Model gauge group, anomalies
Sources
- Quantum field theory — Wikipedia: Quantum field theory (2026-04-10)
- Gauge theory — Wikipedia: Gauge theory (2026-04-10)