Geometric Algebra and Applications to Physics (Hardcover)

THE BASIS FOR GEOMETRIC ALGEBRA
Introduction
Genesis of Geometric Algebra
Mathematical Elements of Geometric Algebra
Geometric Algebra as a Symbolic System
Geometric Algebra as an Axiomatic System (Axiom A)
Some Essential Formulas and Definitions

MULTIVECTORS
Geometric Product of Two Bivectors A and B
Operation of Reversion
Magnitude of a Multivector
Directions and Projections
Angles and Exponential Functions (as Operators)
Exponential Functions of Multivectors

EUCLIDEAN PLANE
The Algebra of Euclidean Plane
Geometric Interpretation of a Bivector of Euclidean Plane
Spinor i-Plane
Distinction between Vector and Spinor Planes
The Geometric Algebra of a Plane

THE PSEUDOSCALAR AND IMAGINARY UNIT
The Geometric Algebra of Euclidean 3-Space
Complex Conjugation
Appendix: Some Important Results

REAL DIRAC ALGEBRA
Geometric Significance of the Dirac Matrices ?μ
Geometric Algebra of Space-Time
Conjugations
Lorentz Rotations
Spinor Theory of Rotations in Three-Dimensional Euclidean Space

SPINOR AND QUATERNION ALGEBRA
Spinor Algebra: Quaternion Algebra
Vector Algebra
Clifford Algebra: Grand Synthesis of Algebra of Grassmann and Hamilton and the Geometric Algebra of Hestenes

MAXWELL EQUATIONS
Maxwell Equations in Minkowski Space-Time
Maxwell Equations in Riemann Sace-Time (V4 Manifold)
Maxwell Equations in Riemann-Cartan Space-Time (U4 Manifold)
Maxwell Equations in Terms of Space-Time Algebra (STA)

ELECTROMAGNETIC FIELD IN SPACE AND TIME (POLARIZATION OF ELECTROMAGNETIC WAVES)
Electromagnetic (EM) Waves and Geometric Algebra
Polarization of Electromagnetic Waves
Quaternion Form of Maxwell Equations from the Spinor Form of STA
Maxwell Equations in Vector Algebra from the Quaternion (Spinor) Formalism
Majorana-Weyl Equations from the Quaternion (Spinor) Formalism of Maxwell Equations
Appendix A: Complex Numbers in Electrodynamics
Appendix B: Plane-Wave Solutions to Maxwell Equations-Polarization of EM Waves

GENERAL OBSERVATIONS AND GENERATORS OF ROTATIONS (NEUTRON INTERFEROMETER EXPERIMENT)
Review of Space-Time Algebra (STA)
The Dirac Equation without Complex Numbers
Observables and the Wave Function
Generators of Rotations in Space-Time: Intrinsic Spin
Fiber Bundles and Quantum Theory vis-a-vis the Geometric Algebra Approach
Fiber Bundle Picture of the Neutron Interferometer Experiment
Charge Conjugation
Appendix

QUANTUM GRAVITY IN REAL SPACE-TIME (COMMUTATORS AND ANTICOMMUTATORS)
Quantum Gravity and Geometric Algebra
Quantum Gravity and Torsion
Quantum Gravity in Real Space-Time
A Quadratic Hamiltonian
Spin Fluctuations
Some Remarks and Conclusions
Appendix: Commutator and Anticommutator

INDEX

References appear at the end of each chapter.