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Geometric Algebra and its Application to Mathematical Physics by Chris J. L. Doran

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Geometric Algebra and its Application to Mathematical Physics written by Chris J. L. Doran, Sidney Sussex College, A dissertation submitted for the degree of Doctor of Philosophy in the University of Cambridge. This is an other great mathematics book cover the following topics.

Introduction
Some History and Recent Developments, Axioms and Definitions, The Geometric Product, The Geometric Algebra of the Plane, The Geometric Algebra of Space, Reflections and Rotations, The Geometric Algebra of Spacetime, Linear Algebra, Linear Functions and the Outermorphism, Non-Orthonormal Frames

Grassmann Algebra and Berezin Calculus
Grassmann Algebra versus Clifford Algebra, The Geometrisation of Berezin Calculus, Example I. The “Grauss” Integral, Example II. The Grassmann Fourier Transform, Some Further Developments

Lie Groups and Spin Groups
Spin Groups and their Generators, The Unitary Group as a Spin Group, The General Linear Group as a Spin Group, Endomorphisms of

Spinor Algebra
Pauli Spinors, Pauli Operators, Multiparticle Pauli States, The Non-Relativistic Singlet State, Non-Relativistic Multiparticle Observables, Dirac Spinors, Changes of Representation — Weyl Spinors, The Multiparticle Spacetime Algebra, The Lorentz Singlet State, 2-Spinor Calculus, 2-Spinor Observables, The 2-spinor Inner Product, The Null Tetrad, The ?A0A Operator, Applications

Point-particle Lagrangians
The Multivector Derivative, Scalar and Multivector Lagrangians, Noether’s Theorem, Scalar Parameterised Transformations, Multivector Parameterised Transformations, Applications — Models for Spinning Point Particles

Field Theory
The Field Equations and Noether’s Theorem, Spacetime Transformations and their Conjugate Tensors, Applications, Multivector Techniques for Functional Differentiation . . . . . . . . 175

Gravity as a Gauge Theory
Gauge Theories and Gravity, Local Poincaré Invariance, Gravitational Action and the Field Equations, The Matter-Field Equations, Comparison with Other Approaches, Point Source Solutions, Radially-Symmetric Static Solutions, Kerr-Type Solutions, Extended Matter Distributions, Conclusions

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