External
Applied Geometric Algebra (Tisza)
Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These course notes attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools.
- Author
- László Tisza
- Publisher
- Massachusetts Institute of Technology
- Source
- LibreTexts
- License
- CC BY-NC-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 30 sections
- 01: Algebraic Preliminaries
- 1.01: Groups
- 1.02: The geometry of the three-dimensional rotation group. The Rodrigues-Hamilton theorem
- 1.03: The n-dimensional vector space V(n)
- 1.04: How to multiply vectors Heuristic considerations
- 1.05: A short survey of linear groups
- 1.06: The unimodular group SL(n R) and the invariance of volume
- 1.07: On alias and alibi. The Object Group
- 02: The Lorentz Group and the Pauli Algebra
- 2.01: Introduction to Lorentz Group and the Pauli Algebra
- 2.02: The Corpuscular Aspects of Light
- 2.03: On Circular and Hyperbolic Rotations
- 2.04: The Pauli Algebra
- 03: Pauli Algebra and Electrodynamics
- 3.01: Lorentz Transformation and Lorentz force
- 3.02: The Free Maxwell Field
- 04: Spinor Calculus
- 4.01: From triads and Euler angles to spinors. A heuristic introduction
- 4.02: Rigid Body Rotation
- 4.03: Polarized light
- 4.04: Relativistic triads and spinors. A preliminary discussion
- 4.05: Review of SU(2) and preview of quantization
- 05: Supplementary Material on the Pauli Algebra
- 5.01: Useful formulas
- 5.02: Lorentz invariance and bilateral multiplication
- 5.03: Typical Examples
- 5.04: On the us of Involutions
- 5.05: On Parameterization and Integration
- 06: Problems
- 6.01: Problems