Waves, Particles and Fields

Introducing Quantum Field Theory

Anthony C. Fischer-Cripps

• Publisher: CRC Press
• Year: 2019
• Print ISBN: 9780367198763
• eBook ISBN: 9780429534072
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

Choice Outstanding Title, September 2020

This book fills a gap in the middle ground between quantum mechanics of a single electron to the concept of a quantum field. In doing so, the book is divided into two parts; the first provides the necessary background to quantum theory extending from Planck's formulation of black body radiation to Schrodinger's equation; and the second part explores Dirac's relativistic electron to quantum fields, finishing with an description of Feynman diagrams and their meaning.

Much more than a popular account, yet not too heavy so as to be inaccessible, this book assumes no prior knowledge of quantum physics or field theory and provides the necessary foundations for readers to then progress to more advanced texts on quantum field theory. It will be of interest to undergraduate students in physics and mathematics, in addition to an interested, general audience.

Features:

• Provides an extensive yet accessible background to the concepts
• Contains numerous, illustrative diagrams
• Presents in-depth explanations of difficult subjects

Mathematics 1

1.1 Introduction

Physics is largely written in the language of mathematics, which generally makes it inaccessible to those who don’t have the opportunity to learn the language. In this book, it is assumed that a middle-level high-school level of mathematics is known to the reader. You should be familiar with the basic methods of differentiation and integration. In Part 1 of this book, we venture beyond that into what might be called first-year college-level mathematics. In Part 2, we go a little further. As we go on, the apparent complexity arises more from the numerous conventions of notation rather than new mathematical theorems. Familiarity with the notation will make things easier to understand.

But, in order to begin, we need to know the language. The aim is to go deep enough to be intellectually satisfying, but not so deep as to be impenetrable.

1.2 Complex Numbers

1.2.1 Complex Numbers

Real numbers are the set of all the numbers, positive and negative, integers and fractions, from negative infinity to positive infinity, including zero, including rational and irrational numbers. These are the numbers we are usually familiar with.

Imaginary numbers are a duplicate set of all these numbers but are kept separated from the set of real numbers. There is nothing “imaginary” about imaginary numbers, this is just a label that distinguishes them from the se...

Table of contents

• Cover
• Half-Title
• Title
• Copyright
• Contents
• Acknowledgements
• 1 Mathematics
• 2 Waves
• 3 Electromagnetic Waves
• 4 Kinetic Theory of Gases
• 5 Quantum Theory
• 6 The Bohr Atom
• 7 The New Quantum Theory
• 8 Relativity
• 9 Advanced Mathematics
• 10 Relativistic Quantum Mechanics
• 11 Probability Flow
• 12 Wave Functions and Spinors
• 13 Classical Field Theory
• 14 Lorentz Invariance
• 15 The Electromagnetic Field
• 16 The Quantum Field
• 17 Feynman Diagrams
• 18 Conclusion
• Appendix
• Index