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.

Concept Map

ConceptNoteTypeDepends OnKey Result
Wave functions, operators, Born rule, Schrödinger equationQuantum Mechanics - OverviewoverviewQM predicts probabilities, not certainties; states live in Hilbert space
Hilbert space, observables, uncertainty principle, entanglementQuantum Mechanics - Mathematical FormalismconceptQuantum Mechanics - OverviewPosition and momentum cannot both be precisely known:
Wave-particle duality, tunneling, double slit, Bell’s theoremQuantum Mechanics - Key PhenomenaconceptQuantum Mechanics - Overview, Quantum Mechanics - Mathematical FormalismNo local hidden variable theory is consistent with experiment
QFT as QM + special relativity + field theoryQuantum Field Theory - OverviewoverviewQuantum Mechanics - OverviewParticles are excitations of quantum fields; particle number can change
QED, Feynman diagrams, renormalizationQED and RenormalizationconceptQuantum Field Theory - Overview, Quantum Mechanics - Mathematical FormalismDivergences removed by redefining mass/charge; QED accurate to 1 in 10^12
Gauge symmetry, local vs global, fiber bundlesGauge Theory - OverviewconceptQuantum Field Theory - Overview, Quantum Mechanics - OverviewLocal symmetry forces the existence of gauge fields and interactions
Standard Model: U(1)×SU(2)×SU(3), gauge bosonsStandard Model and Gauge GroupsconceptGauge Theory - Overview, QED and RenormalizationAll 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

See Also