Physicists spend their undergraduate years learning about classical mechanics, electromagnetism, and quantum mechanics. Each theory has its own rationale --- complete, coherent and consistent. Yet each describes processes in the same physical world, and so must somehow fit into a unified framework. How can we make quantum mechanics obey causality --- special relativity --- like electromagnetism does? In what sense do photons, the quanta explaining the photoelectric effect, obey Maxwell's field equations? Can we build a quantum theory with Maxwell's equations as its classical limit?
These questions motivate quantum field theory. In Physics 380G, we see how ``relativizing'' quantum mechanics implies a world with particles and antiparticles, spontaneously created and annihilated. In the full, multiparticle quantum field theory, we learn the origins of Bose-Einstein and Fermi-Dirac statistics. We find theories whose interactions emerge entirely from symmetry principles. We explore these symmetries --- discrete and continuous, abelian and nonabelian, global and gauged. We see how electromagnetism describes particles with gauged U(1) phase symmetry; and the strong interactions, particles with gauged nonabelian SU(3) symmetry. We study spontaneous symmetry breaking and the Higgs mechanism: how a theory's ground state can become less symmetric than its physical laws, and make some gauge particles massive. We see how this arises in the standard model of the electroweak interactions. Finally, we describe the perturbative treatment of multiparticle interactions through Feynman diagrams.
This course is primarily conceptual, with emphasis on construction and interpretation of formalism (not on detailed calculation). Graduate students are welcome; they may find coverage of the Klein-Gordon and Dirac equations somewhat familiar. This introductory material, which includes brief pointed overviews of classical and quantum physics, electromagnetism and special relativity, as well as early relativizations of quantum mechanics --- should occupy the first third of the course. The rest of the course, involving group theory and the the quantum field theories that describe the particle interactions, should be new material for all students.