| p. 1 |
| The Basis for Geometric Algebra | p. 3 |
| Introduction | p. 3 |
| Genesis of Geometric Algebra | p. 4 |
| Mathematical Elements of Geometric Algebra | p. 10 |
| Geometric Algebra as a Symbolic System | p. 13 |
| Geometric Algebra as an Axiomatic System (Axiom A) | p. 18 |
| Some Essential Formulas and Definitions | p. 23 |
| References | p. 26 |
| Multivectors | p. 27 |
| Geometric Product of Two Bivectors A and B | p. 27 |
| Operation of Reversion | p. 29 |
| Magnitude of a Multivector | p. 30 |
| Directions and Projections | p. 30 |
| Angles and Exponential Functions (as Operators) | p. 34 |
| Exponential Functions of Multivectors | p. 37 |
| References | p. 39 |
| Euclidean Plane | p. 41 |
| The Algebra of Euclidean Plane | p. 41 |
| Geometric Interpretation of a Bivector of Euclidean Plane | p. 44 |
| Spinor i-Plane | p. 45 |
| Correspondence between the i-Plane of Vectors and the Spinor Plane | p. 47 |
| Distinction between Vector and Spinor Planes | p. 47 |
| Some Observations | p. 49 |
| The Geometric Algebra of a Plane | p. 50 |
| References | p. 51 |
| The Pseudoscalar and Imaginary Unit | p. 53 |
| The Geometric Algebra of Euclidean 3-Space | p. 53 |
| The Pseudoscalar of E3 | p. 56 |
| Complex Conjugation | p. 57 |
| Some Important Results | p. 57 |
| References | p. 58 |
| Real Dirac Algebra | p. 59 |
| Geometric Significance of the Dirac Matrices[gamma subscript Mu] | p. 59 |
| Geometric Algebra of Space-Time | p. 60 |
| Conjugations | p. 64 |
| Conjugate Multivectors (Reversion) | p. 64 |
| Space-Time Conjugation | p. 65 |
| Space Conjugation | p. 65 |
| Hermitian Conjugation | p. 65 |
| Lorentz Rotations | p. 66 |
| Spinor Theory of Rotations in Three-Dimensional Euclidean Space | p. 69 |
| References | p. 72 |
| Spinor and Quaternion Algebra | p. 75 |
| Spinor Algebra: Quaternion Algebra | p. 75 |
| Vector Algebra | p. 77 |
| Clifford Algebra: Grand Synthesis of Algebra of Grassmann and Hamilton and the Geometric Algebra of Hestenes | p. 78 |
| References | p. 80 |
| p. 81 |
| Maxwell Equations | p. 83 |
| Maxwell Equations in Minkowski Space-Time | p. 83 |
| Maxwell Equations in Riemann Space-Time (V[subscript 4] Manifold) | p. 85 |
| Maxwell Equations in Riemann-Cartan Space-Time (U[subscript 4] Manifold) | p. 86 |
| Maxwell Equations in Terms of Space-Time Algebra (STA) | p. 88 |
| References | p. 91 |
| Electromagnetic Field in Space and Time (Polarization of Electromagnetic Waves) | p. 93 |
| Electromagnetic (e.m.) Waves and Geometric Algebra | p. 93 |
| Polarization of Electromagnetic Waves | p. 94 |
| Quaternion Form of Maxwell Equations from the Spinor Form of STA | p. 97 |
| Maxwell Equations in Vector Algebra from the Quaternion (Spinor) Formalism | p. 99 |
| Majorana-Weyl Equations from the Quaternion (Spinor) Formalism of Maxwell Equations | p. 100 |
| Complex Numbers in Electrodynamics | p. 103 |
| Plane-Wave Solutions to Maxwell Equations - Polarization of e.m. Waves | p. 105 |
| References | p. 107 |
| General Observations and Generators of Rotations (Neutron Interferometer Experiment) | p. 109 |
| Review of Space-Time Algebra (STA) | p. 109 |
| Note | p. 110 |
| Multivectors | p. 111 |
| Reversion | p. 111 |
| Lorentz Rotation R | p. 111 |
| Two Special Classes of Lorentz Rotations: Boosts and Spatial Rotations | p. 112 |
| Magnitude | p. 112 |
| The Algebra of a Euclidean Plane | p. 113 |
| The Algebra of Euclidean 3-Space | p. 114 |
| The Algebra of Space-Time | p. 116 |
| The Dirac Equation without Complex Numbers | p. 116 |
| Observables and the Wave Function | p. 118 |
| Generators of Rotations in Space-Time: Intrinsic Spin | p. 120 |
| General Observations | p. 121 |
| Fiber Bundles and Quantum Theory vis-a-vis the Geometric Algebra Approach | p. 122 |
| Fiber Bundle Picture of the Neutron Interferometer Experiment | p. 122 |
| Multivector Algebra | p. 125 |
| Lorentz Rotations | p. 127 |
| Conclusion | p. 129 |
| Charge Conjugation | p. 132 |
| p. 133 |
| References | p. 134 |
| Quantum Gravity in Real Space-Time (Commutators and Anticommutators) | p. 137 |
| Quantum Gravity and Geometric Algebra | p. 137 |
| Quantum Gravity and Torsion | p. 140 |
| Quantum Gravity in Real Space-Time | p. 142 |
| A Quadratic Hamiltonian | p. 146 |
| Spin Fluctuations | p. 149 |
| Some Remarks and Conclusions | p. 154 |
| Commutator and Anticommutator | p. 156 |
| References | p. 158 |
| Index | p. 159 |
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