Relativity in Clifford's Geometric Algebras of Space and Spacetime

@article{Baylis2004RelativityIC,
  title={Relativity in Clifford's Geometric Algebras of Space and Spacetime},
  author={William E. Baylis and Garret Sobczyk},
  journal={International Journal of Theoretical Physics},
  year={2004},
  volume={43},
  pages={2061-2079}
}
Of the various formalisms developed to treat relativistic phenomena, those based on Clifford's geometric algebra are especially well adapted for clear geometric interpretations and computational efficiency. Here we study relationships between formulations of special relativity in the spacetime algebra (STA) Cℓ1,3 of the underlying Minkowski vector space, and in the algebra of physical space (APS) Cℓ3. STA lends itself to an absolute formulation of relativity, in which paths, fields, and other… 

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References

SHOWING 1-10 OF 11 REFERENCES

Geometric Algebra for Physicists

Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with

Clifford Algebra: A Computational Tool for Physicists

1. A Taste of Clifford Algebra in Euclidean 3-Space 2. A Sample of Clifford Algebra in Minkowski 4-Space 3. Clifford Algebra for Flat n-Dimensional Spaces 4. Curved Spaces Embedded in Higher

Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics

1 / Geometric Algebra.- 1-1. Axioms, Definitions and Identities.- 1-2. Vector Spaces, Pseudoscalars and Projections.- 1-3. Frames and Matrices.- 1-4. Alternating Forms and Determinants.- 1-5.

Clifford algebra: What is it?

  • E. Bolinder
  • Mathematics
    IEEE Antennas and Propagation Society Newsletter
  • 1987
TLDR
The participants, about 70 people from 20 countries constituted a motley crowd of mathematicians, physicists, and engineers, and the Proceedings of the workshop has been published as a book.

Quaternionic and Clifford Calculus for Physicists and Engineers

Electrodynamics: A modern geometric approach

Phys

  • 15, 1768–1777
  • 1974

Phys

  • Letters A :45–48 Jul
  • 1981

Acta Phys

  • Pol., Vol.B12, 509-521
  • 1981