Quantum Field Theory

Quantum field theory, which started with Paul Dirac's work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity.

Results in Relativistic Quantum Mechanics.- The Construction of Fields.- Canonical Quantization.- Commutators and Propagators.- Interactions and the S-matrix.- The Electromagnetic Field.- Examples of Scattering Processes.- Functional Integral Representations.- Renormalization.- Gauge Theories.- Symmetry.- Spontaneous symmetry breaking.- Anomalies I.- Elements of differential geometry.- Path Integrals.- The Configuration Space in Nonabelian Gauge Theory.- Anomalies II.- Finite temperature and density.- Gauge theory: Nonperturbative questions.- Elements of Geometric Quantization.