Theoretical Physics
Routing Summary
This folder covers foundational theoretical physics: quantum mechanics, quantum field theory, and gauge theory, drawn from Wikipedia overviews. Contains 9 notes.
- Need QM foundations (wave functions, Schrödinger, uncertainty)? → Quantum Mechanics - Overview
- Need QM formalism (Hilbert space, operators, Born rule)? → Quantum Mechanics - Mathematical Formalism
- Need QM phenomena (entanglement, tunneling, wave-particle duality)? → Quantum Mechanics - Key Phenomena
- Need QFT overview (fields, quantization, Standard Model)? → Quantum Field Theory - Overview
- Need renormalization and Feynman diagrams? → QED and Renormalization
- Need gauge symmetry and gauge bosons? → Gauge Theory - Overview
- Need the Standard Model gauge structure? → Standard Model and Gauge Groups
Concept Map
| Concept | Note | Type | Depends On | Key Result |
|---|---|---|---|---|
| Wave functions, operators, Born rule, Schrödinger equation | Quantum Mechanics - Overview | overview | — | QM predicts probabilities, not certainties; states live in Hilbert space |
| Hilbert space, observables, uncertainty principle, entanglement | Quantum Mechanics - Mathematical Formalism | concept | Quantum Mechanics - Overview | Position and momentum cannot both be precisely known: |
| Wave-particle duality, tunneling, double slit, Bell’s theorem | Quantum Mechanics - Key Phenomena | concept | Quantum Mechanics - Overview, Quantum Mechanics - Mathematical Formalism | No local hidden variable theory is consistent with experiment |
| QFT as QM + special relativity + field theory | Quantum Field Theory - Overview | overview | Quantum Mechanics - Overview | Particles are excitations of quantum fields; particle number can change |
| QED, Feynman diagrams, renormalization | QED and Renormalization | concept | Quantum Field Theory - Overview, Quantum Mechanics - Mathematical Formalism | Divergences removed by redefining mass/charge; QED accurate to 1 in 10^12 |
| Gauge symmetry, local vs global, fiber bundles | Gauge Theory - Overview | concept | Quantum Field Theory - Overview, Quantum Mechanics - Overview | Local symmetry forces the existence of gauge fields and interactions |
| 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 Mechanics - Overview — CONTAINS: QM historical development, wave functions, Schrödinger equation, time evolution, examples (free particle, harmonic oscillator)
- Quantum Mechanics - Mathematical Formalism — CONTAINS: Hilbert space formalism, observables as Hermitian operators, Born rule, uncertainty principle, composite systems, entanglement, Noether theorem in QM
- Quantum Mechanics - Key Phenomena — CONTAINS: Wave-particle duality, double-slit experiment, quantum tunneling, quantum interference, Bell’s theorem, quantum entanglement, decoherence
- Quantum Field Theory - Overview — CONTAINS: QFT historical development, canonical quantization, QED, Dirac equation, antimatter, Standard Model
- QED and Renormalization — CONTAINS: Perturbative infinities, renormalization procedure, Lamb shift, Feynman diagrams, anomalous magnetic moment, path integral formulation
- Gauge Theory - Overview — CONTAINS: Global vs local symmetry, gauge fields, Lie groups, covariant derivative, gauge invariance, fiber bundles
- Standard Model and Gauge Groups — CONTAINS: Yang-Mills theory, QCD, electroweak unification, gauge bosons (photon, W/Z, gluons), Higgs mechanism
Sources
- Quantum mechanics — Wikipedia: Quantum mechanics (comprehensive overview)
- Quantum field theory — Wikipedia: Quantum field theory (comprehensive overview)
- Gauge theory — Wikipedia: Gauge theory (comprehensive overview)
See Also
- Research — Top-level research index