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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 **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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