Professor Susskind closes the course with the presentation of the quantum field theory for spin-1/2 fermions. This theory is based on the Dirac equation, which, when Dirac developed it in 1928, was the first thory to account fully for special relativity in the context of quantum mechanics. This theory explains spin as a consequaence of of the union of quantum mechanics and relativity, and also led to the theory of antimatter and ultimate discovery of the first antimatter particle - the positron.
Professor Susskind begins the presentation by reviewing the Dirac equation for an electron in one dimension, and then generalizes this to derive the therory for three dimensions. This led Dirac to develop his 4x4 gamma matrices. In Dirac's theory, the mass of fermions originates from the cross term between the two chiralities in 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.