Logarithm of multivector in real 3D Clifford algebras
Rings and Algebras
2023-05-17 v1 Mathematical Physics
math.MP
Abstract
Closed form expressions for a logarithm of general multivector (MV) in base-free form in real geometric algebras (GAs) Cl(p,q) are presented for all n=p+q=3. In contrast to logarithm of complex numbers (isomorphic to Cl(0,1), 3D logarithmic functions, due to appearance of two double angle arc tangent functions, allow to include two sets of sheets characterized by discrete coefficients. Formulas for generic and special cases of individual blades and their combinations are provided.
Cite
@article{arxiv.2305.09469,
title = {Logarithm of multivector in real 3D Clifford algebras},
author = {A. Acus and A. Dargys},
journal= {arXiv preprint arXiv:2305.09469},
year = {2023}
}
Comments
27 pages, 1 figure