Notes for Math 635: Topological Quantum Field Theory
نویسنده
چکیده
The goal of this course is to define invariants of 3-manifolds and knots and representations of the mapping class group, using quantum field theory. We will follow Kohno, Conformal Field Theory and Topology, supplementing it with additional material to make it more accessible. The amount of mathematics that goes into defining these invariants is rather substantial (especially for the geometric approach that we will be taking), and we will spend a considerable amount of time on the preliminaries.
منابع مشابه
Notes on Topological Quantum Field Theory
These notes are meant to provide an introduction to topological quantum field theory for mathematicians. Topics include applications of Chern-Simons theory to the study of knots and Atiyah’s definition of a topological quantum field theory. We also include a self-contained introduction to Yang-Mills theory for physical motivation.
متن کاملUndergraduate Lecture Notes in Topological Quantum Field Theory
These third–year lecture notes are designed for a 1–semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second–year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism.
متن کاملIntersection Theory , Integrable Hierarchies and Topological Field Theory ∗
In these lecture notes we review the various relations between intersection theory on the moduli space of Riemann surfaces, integrable hierarchies of KdV type, matrix models, and topological field theory. We focus in particular on the question why matrix integrals of the type considered by Kontsevich naturally appear as τ -functions of integrable hierarchies related to topological minimal model...
متن کاملA mini-course on topological strings
These are the lecture notes for a short course in topological string theory that I gave at Uppsala University in the fall of 2004. The notes are aimed at PhD students who have studied quantum field theory and general relativity, and who have some general knowledge of ordinary string theory. The main purpose of the course is to cover the basics: after a review of the necessary mathematical tools...
متن کاملMath and Physics
I present a brief review on some of the recent developments in topological quantum field theory. These include topological string theory, topological Yang-Mills theory and Chern-Simons gauge theory. It is emphasized how the application of different field and string theory methods has led to important progress, opening entirely new points of view in the context of Gromov-Witten invariants, Donal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006