Professor Susskind presents the Hamiltonian for a quantum field, and demonstrates how these Hamiltonians describe particle interactions such as decay and scattering. He then introduces the field theory for fermions by deriving the Dirac equation. The theory behind the Dirac equations was the first theory to account fully for special relativity in the context of quantum mechanics. This relativistic Schrödinger equation implies the existence of antimatter.

Recorded on November 18, 2013.

Topics:
- Hamiltonian
- Dirac equation
- Klein-Gordon equation
- Antimatter

1. Review of quantum mechanics and introduction to symmetry
2. Symmetry groups and degeneracy
3. Atomic orbits and harmonic oscillators
4. Spin, Pauli Matrices, and Pauli Exclusion Principle
5. Fermions: a tale of two minus signs
6. Quantum Field Theory: Particle Creation and Annihilation Operators
7. Quantum Field Theory: Fermions and Bosons
8. Second Quantization
9. Quantum Field Hamiltonian
10. Fermions and the Dirac equation

This course will explore the various types of quantum systems that occur in nature, from harmonic oscillators to atoms and molecules, photons, and quantum fields. Students will learn what it means for an electron to be a fermion and how that leads to the Pauli exclusion principle. They will also learn what it means for a photon to be a boson and how that allows us to build radios and lasers. The strange phenomenon of quantum tunneling will lead to an understanding of how nuclei emit alpha particles and how the same effect predicts that cosmological space can “boil.” Finally, the course will delve into the world of quantum field theory and the relation between waves and particles.