Many-body physics
Graduate · Physics
Syllabus focus
Topics typically covered
Theoretical / proof-based
Second quantization
- Fock space formalism for fermions and bosons
- Field operators and commutation relations
- Basis transformations and normal ordering
- Coherent states and path integrals
- Hubbard model as canonical example
Green's functions
- Retarded and advanced propagators
- Dyson equation and self-energy
- Spectral functions and sum rules
- Lehmann representation
- Analytic continuation to real frequencies
Diagrammatic methods
- Feynman diagrams at zero and finite T
- Wick's theorem for fermions
- Random phase approximation
- BCS gap equation from Nambu formalism
- Strongly correlated regimes: Mott transition (intro)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Second quantization
Fock space formalism for fermions and bosons
Coming soon - Green's functions
Retarded and advanced propagators
Coming soon - Diagrammatic methods
Feynman diagrams at zero and finite T
Coming soon
Notes
Topics reflect common graduate physics core and elective syllabi at US universities. Sequencing and emphasis vary between one- and two-semester treatments.