Vector eld computations in Cli ord's geometric algebra
نویسندگان
چکیده
Exactly 125 years ago G. Peano introduced the modern concept of vectors in his 1888 book "Geometric Calculus According to the Ausdehnungslehre (Theory of Extension) of H. Grassmann". Unknown to Peano, the young British mathematician W. K. Cli ord (1846-1879) in his 1878 work "Applications of Grassmann's Extensive Algebra" had already 10 years earlier perfected Grassmann's algebra to the modern concept of geometric algebras, including the measurement of lengths (areas and volumes) and angles (between arbitrary subspaces). This leads currently to new ideal methods for vector eld computations in geometric algebra, of which several recent exemplary results will be introduced.
منابع مشابه
Cli ord geometric parameterization of inequivalent vacua
We propose a geometric method to parameterize inequivalent vacua. Introducing Cli ord algebras with arbitrary bilinear forms we distinguish isomorphic algebras {as Cli ord algebras{ by di erent ltrations resp. induced gradings. The idea of a vacuum is introduced as the unique algebraic projection on the base eld embedded in the Cli ord algebra. The parameterization of inequivalent vacua takes p...
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