Introduction to Part I

Franco Strocchi

Peter Millington

Tai Kai Ng

PART I 1. Introduction 2. Lagrangian Formulation of Classical Mechanics and Field Theory 3. Quantization of Classical Field Theory I 4. Quantization of Classical Field Theory II 5. Berry Phase and Gauge Theory 6. Introduction to Perturbation Theory PART II 7. Concept of Effective Field Theory, Phases, and Phase Transition 8. Non-Linear Effects and Topology in Quantum Field Theory 9. Simple Bose Liquids - Introduction to Superfluidity 10. Simple Fermi Liquids - Introduction to Fermi Liquid Theory 11. Introduction to BCS Theory (S-Wave Superconductors) 12. Introduction to Quantum Magnetism

Vanderlei Salvador Bagnato, K. M. F. Magalhães, Jorge Amin Seman +5 more

This text corresponds to part of the course presented at the ELAF XXXVIII. It is composed of work previously done along the years. The level of this introduction follows the last year of undergraduate and first year of graduate courses. We apologize to the experts on this field, but the idea here is to provide the basic principles and tools for students just getting involved with this topic. For those interested in a deeper reading on the subject, we strongly recommend the review article published by Courteille, Bagnato and Yukalov [1] from which part of this text was extracted. The lecture is divided in three parts: an introduction, the basic concepts of Bose‐Einstein Condensation and information about making and probing BECs.

Alexander A. Lisyansky, E. S. Andrianov, Alexey P. Vinogradov +1 more

Gerald W. Johnson, Michel L. Lapidus, Lance Nielsen

Abstract The first part of the introduction provides a (short) historical overview of Feynman’s development of his operational calculus, i.e. the formation of functions of several not necessarily commuting operators. This is done using quotes from Feynman’s Nobel lecture, as well as from biographical information and parts of Feynman’s early papers. This portion of the introduction will aid the reader not familiar with Feynman’s ideas to gain some insight into their intellectual and physical origins. After this historical sketch of the origins of the operational calculus, we take the time to introduce, via simple examples, Feynman’s time-ordering convention and Feynman’s heuristic “rules.” The remainder of the introduction is devoted to a rather detailed chapter-by-chapter description of the contents of this volume.