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Path Integral Methods and Applications
(24.04.2000)
Аннотация
These lectures are intended as an introduction to the technique of path
integrals and their applications in physics. The audience is mainly first-year
graduate students, and it is assumed that the reader has a good foundation in
quantum mechanics. No prior exposure to path integrals is assumed, however.
The path integral is a formulation of quantum mechanics equivalent to the
standard formulations, offering a new way of looking at the subject which is,
arguably, more intuitive than the usual approaches. Applications of path
integrals are as vast as those of quantum mechanics itself, including the
quantum mechanics of a single particle, statistical mechanics, condensed matter
physics and quantum field theory.
After an introduction including a very brief historical overview of the
subject, we derive a path integral expression for the propagator in quantum
mechanics, including the free particle and harmonic oscillator as examples. We
then discuss a variety of applications, including path integrals in
multiply-connected spaces, Euclidean path integrals and statistical mechanics,
perturbation theory in quantum mechanics and in quantum field theory, and
instantons via path integrals.
For the most part, the emphasis is on explicit calculations in the familiar
setting of quantum mechanics, with some discussion (often brief and schematic)
of how these ideas can be applied to more complicated situations such as field
theory.
