Welcome to the home page of QFT I for Spring 2016. Quantum field theory is the mathematical framework of all of particle physics and the indispensable language of a large body of statistical mechanics and of quantum many body physics. It is an incredibly rich subject that you will keep learning for the rest of your scientific life.
Learning QFT is qualitatively different from learning other advanced subjects, such as quantum mechanics and classical general relativity, which have a more established logical framework, and have been formalized even to the satisfaction of mathematicians. QFT is still an open subject, close to the conceptual frontier of theoretical physics. It is a work in progress, enriched by new viewpoints, simplified and extended in unexpected directions by each generation of theorists.
There are simply too many fundamental ideas and techniques for a two-semester course to be comprehensive. My aim in this first semester will be to expose you as fast as possible (but hopefully not faster) to the basic formalism and techniques of perturbative quantum field theory: field quantization (both in the canonical and path-integral approach), Feynman diagrams, symmetries, the basics of renormalization theory. We will apply the formalism mostly to particle physics examples, with the goal of covering some of the classic calculations of Quantum Electrodynamics (the quantum theory of light and electrons) by the end of the semester. (The physics of non-abelian gauge fields and the Standard Model of particle physics will be covered in the second semester.) But we will also see how to apply QFT to the calculation of critical exponents in statistical mechanics. That the same formalism should predict the scattering of relativistic particles and the critical exponents of boiling water is one of the main wonders of the subject.
Course Outline: The necessity of the field viewpoint. Canonical quantization of the scalar field. Symmetries and Noether's theorem. Path-integral quantization. Diagrammatics: connected, 1P1, Feynman rules. S-matrix and cross sections. Representations of the Poincare' group. Canonical and path-integral quantization of spinors. Abelian gauge fields. Quantum Electrodynamics (QED). Tree-level processes in QED. Renormalization of scalar field theory. The renormalization group. The Wilson-Fisher fixed point and critical exponents. If time permits: spontaneous breaking of global symmetries; Coleman-Weinberg potential.
Discussion of the homework is encouraged but each of you must submit a personal solution.
Midterm Exam March 29 in class
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