Lectures on Functional Integration
Given at the University of Florida, Spring Semester 2004.
Functional integration is a tool useful to study general diffusion processes, quantum mechanics, and quantum field theory, among other applications. The mathematics of such integrals can be studied largely independently of specific applications, and this approach minimizes the prerequisites needed to follow the material. Although some knowledge of quantum mechanics would prove useful, the material is presented so that most of what is needed is included. The course is designed for a physics audience, with an occasional excursion into material and style of presentation that is more mathematical than a typical physics course might present.
Broadly speaking, topics covered include integration, random variables, stochastic processes, Wiener measure, Feynman path integrals in various forms, a brief survey of scalar quantum field theory, and concludes with the presentation of a soluble mathematical model of a nonrenormalizable quantum field theory that illustrate efforts that currently represent the frontier of research.
Thanks to Khandker Muttalib whose lecture notes appear here.
Audio & image files copyright John Klauder and the University of Florida.
Comments welcome at klauder at phys dot ufl dot edu
Some Recommended Books
G. Roepstorff, "Path Integral Approach to Quantum Physics", Springer-Verlag, Berlin, 1996
R. Feynman and A. Hibbs, "Quantum Mechanics and Path Integrals", McGraw-Hill, New York, 1965
A.V. Skorokhod, "Studies in the Theory of Random Processes", Addison-Wesley Publishing, Reading, Massachusetts, 1965
B. Simon, "Functional Integration and Quantum Physics", Academic Poress, New York, 1979
L. Schulman, "Techniques and Applications of Path Integration'', John Wiley & Sons, New York, 1981
J. Klauder and B-S. Skagerstam, "Coherent States", World Scientific, Singapore, 1985
C. Grosche and F. Steiner, "Handbook of Feynman Path Integrals", Springer-Verlag, Berlin, 1998
J. Klauder, "Beyond Conventional Quantization", Cambridge University Press, Cambridge, 2000
H. Kleinert, "Path Integrals in Quantum Mehcanics, Statistics, and Polymer Physics", 3rd Edition, World Scientific, Singapore, 2003
Lecture Notes & Audio
Audio files are wma format - each lecture is around 50 mins and 12 MB.
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Problem Set 1
Problem Set 2