## Clifford Algebra: A Computational Tool for PhysicistsClifford algebras have become an indispensable tool for physicists at the cutting edge of theoretical investigations. Applications in physics range from special relativity and the rotating top at one end of the spectrum, to general relativity and Dirac's equation for the electron at the other. Clifford algebras have also become a virtual necessity in some areas of physics, and their usefulness is expanding in other areas, such as algebraic manipulations involving Dirac matrices in quantum thermodynamics; Kaluza-Klein theories and dimensional renormalization theories; and the formation of superstring theories. This book, aimed at beginning graduate students in physics and math, introduces readers to the techniques of Clifford algebras. |

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### Contents

3 | |

III | 11 |

IV | 12 |

V | 25 |

VI | 36 |

VII | 41 |

VIII | 44 |

IX | 47 |

XXIII | 144 |

XXIV | 154 |

XXV | 161 |

XXVI | 170 |

XXVII | 180 |

XXVIII | 185 |

XXIX | 189 |

XXX | 204 |

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### Common terms and phrases

2-forms angle appears in Eq arbitrary axis becomes boost operator c-unitary Chapter Christoffel symbols Clifford algebra Clifford functions Clifford number coefficients complex components compute consider constant construct coordinate system cos2 cosh cosh2 curvature 2-forms defined diagonal differential forms Dirac matrices Dirac's equation ds ds eigenvalues eigenvector Einstein's field equations electron example flat space Fock-Ivanenko 2-vectors Furthermore Gaussian curvature geodesic index Dirac matrices indices integral isomorphic Kerr metric last equation linear combination Lorentz transformation m-dimensional surface matrix representation metric tensor Minkowski 4-space multiply noncoordinate notation null plane null vector observer obtain orbit orthogonal orthonormal parallel transport particle Petrov matrix principal null directions pseudo-Euclidean space real Clifford represents restricted Lorentz right-hand side rotation operator scalar Schwarzschild metric side of Eq signature matrix sin2 sinh solution space-time spanned spherical Suppose symmetry system of Dirac tangent vectors theorem universal Clifford algebra velocity zero