From Classical Mechanics To Quantum Field Theory, A Tutorial

✍ Scribed by Manuel Asorey, Elisa Ercolessi, Valter Moretti

• Publisher: World Scientific Publishing Company
• Year: 2019
• Tongue: English
• Leaves: 255
• Category: Library

✦ Synopsis

This book collects an extended version of the lectures delivered by the authors at the Fall Workshop on Geometry and Physics in the years 2014, 2015, 2016.

It aims at introducing advanced graduate and PhD students, as well as young researchers, to current research in mathematics and physics. In particular, it fills the gap between the more physical-oriented and the more mathematical-oriented literature on quantum theory. It introduces various approaches to methods of quantization, along with their impact on modern mathematical methods.

✦ Table of Contents

Preface
Acknowledgments
Contents
1. A Short Course on Quantum Mechanics and Methods of Quantization
1.1 Introduction
1.2 Overview of Quantum Mechanics
1.3 Methods of Quantization
Bibliography
2. Mathematical Foundations of Quantum Mechanics: An Advanced Short Course
2.1 Introduction: Summary of Elementary Facts of QM
2.2 Observables in Infinite Dimensional Hilbert Spaces: Spectral Theory
2.3 More Fundamental Quantum Structures
2.4 Just Few Words about the Algebraic Approach
Bibliography
3. A Concise Introduction to Quantum Field Theory
3.1 Introduction
3.2 Quantum Mechanics and Relativity
3.3 Quantum Field Theory
3.4 The Quantum Vacuum
3.5 Fields versus Particles
3.6 Fields in Interaction
3.7 Covariant Approach
3.8 Conformal Invariant Theories
3.9 What is Beyond?
3.10 Appendix 1 Casimir effect
3.11 Appendix 2. Gaussian measures
3.12 Appendix 3. Peierls brackets
Bibliography
Index