RES.8-001 | Spring 2009 | Undergraduate

Applied Geometric Algebra

Lecture Notes

The complete set of lecture notes is also available as a single file. (PDF - 2.7MB)

  • Table of Contents (PDF)
  • Preface by Samuel Gasster (PDF)

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)

Course Info

As Taught In
Spring 2009
Learning Resource Types
Problem Sets
Online Textbook