Book contents
- Frontmatter
- Dedication
- Contents
- Introduction
- PART I Basics
- Part II Spin
- 8 Representations of the Orthogonal and the Lorentz Group
- 9 Representations of the Poincaré Group
- 10 Basic Free Fields
- Part III Interactions
- Part IV Renormalization
- Part V Complements
- Solutions to Selected Exercises
- Reading Suggestions
- References
- Index
10 - Basic Free Fields
from Part II - Spin
Published online by Cambridge University Press: 22 February 2022
- Frontmatter
- Dedication
- Contents
- Introduction
- PART I Basics
- Part II Spin
- 8 Representations of the Orthogonal and the Lorentz Group
- 9 Representations of the Poincaré Group
- 10 Basic Free Fields
- Part III Interactions
- Part IV Renormalization
- Part V Complements
- Solutions to Selected Exercises
- Reading Suggestions
- References
- Index
Summary
We explain why the experimentally established fact of conservation of electrical charges more or less forces the existence of anti-particles. Armed with this essential information we then turn to the study of Lorentz covariant families of quantum fields, of which the massive scalar field of Chapter 5 is the simplest example. These are the building blocks of the standard model, which describes the whole zoo of existing particles. We follow the steps of S. Weinberg to discover that simple linear algebra, combined with a few natural assumptions is all that is required to discover the main fields which are used by Nature (which we list and study), without having to resort to the contortions often seen in the physics literature. We give an example of these contortions by describing the attempts made to relate the Dirac field to classical mechanics.
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- What Is a Quantum Field Theory? , pp. 250 - 296Publisher: Cambridge University PressPrint publication year: 2022