| Lecture Notes CONTENTS |
|---|
| Chapter 1: Introduction (PDF) |
| Chapter 2: Algebraic Preliminaries (PDF) |
| 2.1 Groups 2.2 The geometry of the three-dimensional rotation group. The Rodrigues-Hamilton theorem 2.3 The n-dimensional vector space V(n) 2.4 How to multiply vectors? Heuristic considerations 2.5 A short survey of linear groups 2.6 The unimodular group SL(n, R) and the invariance of volume 2.7 On “alias” and “alibi”. The Object Group |
| Chapter 3: The Lorentz Group and the Pauli Algebra (PDF) |
| 3.1 Introduction 3.2 The corpuscular aspects of light 3.3 On circular and hyperbolic rotations 3.4 The Pauli Algebra |
| Chapter 4: Pauli Algebra and Electrodynamics (PDF) |
| 4.1 Lorentz transformation and Lorentz force 4.2 The Free Maxwell Field |
| Chapter 5: Spinor Calculus (PDF) |
| 5.1 From triads and Euler angles to spinors. A heuristic introduction 5.2 Rigid Body Rotation 5.3 Polarized light 5.4 Relativistic triads and spinors. A preliminary discussion 5.5 Review of SU(2) and preview of quantization |
| Supplementary Material on the Pauli Algebra (PDF) |
| A.1 Useful formulas A.2 Lorentz invariance and bilateral multiplication A.3 Typical Examples A.4 On the us of Involutions A.5 On Parameterization and Integration |
| Homework Assignments (PDF) |
| References (PDF) |
The complete set of lecture notes is also available as a single file. (PDF - 1.5MB)