The key point of "Second Quantization" is that the expectation value of the hamiltonian with a quantum wavefunction for one particle (for one-body terms) or two particles (for 2-body interaction terms) is "quantized again", writing it as an operator that applies for any number of particles. The creation and annihilation operators obey commutation rules the enforce the proper symmetries. This is of great value in dealing with the myriad terms that appear in perturbation theory expansions for interacting-particle systems.

1. Second quantization
• Field operators for bosons and fermions
• Commutation rules
• Expressions in terms of an orthonormal basis, e.g., plane waves
2. Hamiltonian for interacting electrons
• Interaction terms
• Diagrammatic representation of perturbation expansion for interaction terms - Feynman diagrams
• Example of Jellium
3. Hartree Fock approximation
• Example of Jellium
4. Fundamental problem in series of diagrams