The Theory and Applications of Instanton Calculations

Instantons, or pseudoparticles, are solutions to the equations of motion in classical field theories on a Euclidean spacetime. Instantons are found everywhere in quantum theories as they have many applications in quantum tunnelling. Diverse physical phenomena may be described through quantum tunnelling, for example: the Josephson effect, the decay of meta-stable nuclear states, band formation in tight binding models of crystalline solids, the structure of the gauge theory vacuum, confinement in 2+1 dimensions, and the decay of superheated or supercooled phases. Drawing inspiration from Sidney Colemans Erice lectures, this volume provides an accessible, detailed introduction to instanton methods, with many applications, making it a valuable resource for graduate students in many areas of physics, from condensed matter, particle and nuclear physics, to string theory.

Preface; 1. Introduction; 2. Quantum mechanics and the path integral; 3. The symmetric double well; 4. Decay of a meta-stable state; 5. Quantum field theory and the path integral; 6. Decay of the false vacuum; 7. Large orders in perturbation theory; 8. Quantum electrodynamics in 1+1 dimensions; 9. The Polyakov proof of confinement; 10. Monopole pair production; 11. Quantum chromodynamics (QCD); 12. Instantons, supersymmetry and Morse theory; Appendix A. As aside on 0(4); Appendix B. Asymptotic analysis; Bibliography; Index.