Imaginary numbers are not real—The geometric algebra of spacetime

@article{Gull1993ImaginaryNA,
  title={Imaginary numbers are not real—The geometric algebra of spacetime},
  author={S. Gull and A. Lasenby and C. Doran},
  journal={Foundations of Physics},
  year={1993},
  volume={23},
  pages={1175-1201}
}
This paper contains a tutorial introduction to the ideas of geometric algebra, concentrating on its physical applications. We show how the definition of a “geometric product” of vectors in 2-and 3-dimensional space provides precise geometrical interpretations of the imaginary numbers often used in conventional methods. Reflections and rotations are analyzed in terms of bilinear spinor transformations, and are then related to the theory of analytic functions and their natural extension in more… Expand

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