Instanton Physics

Instantons are a valuable theoretical tool in quantum mechanics and quantum field theory for analyzing tunneling phenomena. This set of lectures is intended for graduate students who wish to study non-perturbative phenomena in a variety of subjects: QFT, QM, chemical physics, neural nets, etc.  

Lecture #1. tunneling; double slit experiment; path integral derivation of quantum amplitude.

Lecture #2. Review of functional analysis; imaginary time, free particle and harmonic oscillator Green’s function.

Lecture #3. Double well potential; fluctuation operator; zero mode; determination of Jacobian; evaluation of fluctuation determinant; dilute gas approximation.

Lecture #4. Decay of a metastable state; bounces; analytic continuation; dilute bounce approximation; probability of tunneling out of unstable vacuum.

Lecture #5. Basic QFT for a scalar field; tunneling of field configurations; O(4) instanton; how/when will the universe end?

Lecture #6. Differential geometry and differential forms; rewriting Maxwell's equations; Einstein-Hilbert action in coordinate free form; relation to gauge theories.

Lecture #7. Instantons in Yang Mills gauge theories; gauge potential; F as a two-form; QCD vacuum.