Leonard Susskind extends the presentation of quantum field theory to multi-particle systems, and derives the particle creation and annihilation operators.

Professor Susskind introduces quantum field theory. Excepting gravity, quantum field theory is our most complete description of the universe. Each quantum field corresponds to a specific particle type, and is represented by a state vector consisting of the number of particles in each possible energy state. These numbers are called occupation numbers. This representation uses the same quantum mathematics as a state vector for multiple harmonic oscillators with the basis vectors being the energy state of each oscillator. Therefore the quantum field mathematics follow those introduced for harmonic oscillators in previous lectures. However, in the case of quantum field theory, the raising and lowering operators become operators which create and destroy particles in a given energy state.

Recorded on November 4, 2013.

Topics:
- Quantum field theory
- Occupation numbers
- Creation and anhilation operators

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.