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Geometric Algebra and its Application to Mathematical Physics by Chris J. L. Doran
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About this book :-
Geometric Algebra and its Application to Mathematical Physics
Chris Doran.
This text is a dissertation submitted for the degree of Doctor of Philosophy in the University of Cambridge.
This is the result of work carried out in the Department of Applied Mathematics and Theoretical Physics between October 1990 and October 1993. Sections of the dissertation have appeared in a series of collaborative papers.
Book Detail :-
Title: Geometric Algebra and its Application to Mathematical Physics
Edition:
Author(s): Chris J. L. Doran
Publisher:
Series:
Year: 1994
Pages: 224
Type: PDF
Language: English
ISBN:
Country:
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Book Contents :-
Geometric Algebra and its Application to Mathematical Physics
Chris Doran
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
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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