Explicit Baker–Campbell–Hausdorff–Dynkin formula for spacetime via geometric algebra

@article{Wilson2021ExplicitBF,
  title={Explicit Baker–Campbell–Hausdorff–Dynkin formula for spacetime via geometric algebra},
  author={Joseph Clement Wilson and Matt Visser},
  journal={International Journal of Geometric Methods in Modern Physics},
  year={2021}
}
  • J. Wilson, M. Visser
  • Published 1 July 2021
  • Mathematics
  • International Journal of Geometric Methods in Modern Physics
We present a compact Baker–Campbell–Hausdorff–Dynkin formula for the composition of Lorentz transformations [Formula: see text] in the spin representation (a.k.a. Lorentz rotors) in terms of their generators [Formula: see text]: [Formula: see text] This formula is general to geometric algebras (a.k.a. real Clifford algebras) of dimension [Formula: see text], naturally generalizing Rodrigues’ formula for rotations in [Formula: see text]. In particular, it applies to Lorentz rotors within the… 
1 Citations
Current survey of Clifford geometric algebra applications
Clifford geometric algebra (GA) and Clifford analysis (also termed geometric calculus (GC)) is a rapidly developing field of pure and applied mathematics. In 2013 a popular survey98 was written about

References

SHOWING 1-10 OF 31 REFERENCES
Imaginary numbers are not real—The geometric algebra of spacetime
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
Geometric algebra and its application to mathematical physics
Clifford algebras have been studied for many years and their algebraic properties are well known. In particular, all Clifford algebras have been classified as matrix algebras over one of the three
Spacetime algebra as a powerful tool for electromagnetism
Composition of Lorentz Transformations in Terms of Their Generators
Two-forms in Minkowski space-time may be considered as generators of Lorentz transformations. Here, the covariant and general expression for the composition law (Baker–Campbell–Hausdorff formula) of
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
Geometric Algebra as a Unifying Language for Physics and Engineering and Its Use in the Study of Gravity
Geometric Algebra (GA) is a mathematical language that aids a unified approach and understanding in topics across mathematics, physics and engineering. In this contribution, we introduce the
Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions
In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic
Geometric algebra for computer graphics
TLDR
John Vince tackles complex numbers and quaternions; the nature of wedge product and geometric product; reflections and rotations; and how to implement lines, planes, volumes and intersections in this accessible and very readable introduction to geometric algebra.
Spacetime physics with geometric algebra
This is an introduction to spacetime algebra (STA) as a unified mathematical language for physics. STA simplifies, extends, and integrates the mathematical methods of classical, relativistic, and
On the exponential of the 2-forms in relativity
A study of intrinsic properties of proper Lorentz tensors (tensor fields defining proper Lorentz transformations at every point of space-time) is made, giving rise to their covariant decompositions.
...
1
2
3
4
...