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

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Geometric Algebra eBooks . We hope mathematician or person who’s interested in mathematics like these books.

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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  • Free
  • English
  • PDF 51
  • Page 92