Nguồn ngoài

Applied Geometric Algebra

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. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics.

Mathematical Physics and Pedagogy Physics

Tác giả: László Tisza
Nhà xuất bản: Massachusetts Institute of Technology
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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Mục lục· 32 mục

01: Introduction
1.01: New Page
02: Algebraic Preliminaries
2.01: Groups
2.02: The geometry of the three-dimensional rotation group. The Rodrigues-Hamilton theorem
2.03: The n-dimensional vector space V(n)
2.04: How to multiply vectors Heuristic considerations
2.05: A short survey of linear groups
2.06: The unimodular group SL(n R) and the invariance of volume
2.07: On alias and alibi. The Object Group
03: The Lorentz Group and the Pauli Algebra
3.01: Introduction
3.02: The corpuscular aspects of light
3.03: On circular and hyperbolic rotations
3.04: The Pauli Algebra
04: Pauli Algebra and Electrodynamics
4.01: Lorentz transformation and Lorentz force
4.02: The Free Maxwell Field
05: Spinor Calculus
5.01: From triads and Euler angles to spinors. A heuristic introduction
5.02: Rigid Body Rotation
5.03: Polarized light
5.04: Relativistic triads and spinors. A preliminary discussion
5.05: Review of SU(2) and preview of quantization
06: Supplementary Material on the Pauli Algebra
6.01: Useful formulas
6.02: Lorentz invariance and bilateral multiplication
6.03: Typical Examples
6.04: On the us of Involutions
6.05: On Parameterization and Integration
07: Homework Assignments
7.01: New Page