Clifford Algebraic Remark on the Mandelbrot Set of Two--Component Number Systems

We investigate with the help of Clifford algebraic methods the Mandelbrot set over arbitrary two-component number systems. The complex numbers are regarded as operator spinors in D\times spin(2) resp. spin(2). The thereby induced (pseudo) normforms and traces are not the usual ones. A multi quadratic set is obtained in the hyperbolic case contrary to [1]. In the hyperbolic case a breakdown of this simple dynamics takes place.Comment: LaTeX, 27 pages, 6 fig. with psfig include

Vertex Normalordering as a Consequence of Nonsymmetric Bilinearforms in Clifford Algebras

We consider Clifford algebras with nonsymmetric bilinear forms, which are isomorphic to the standard symmetric ones, but not equal. Observing, that the content of physical theories is dependent on the injection \oplus^n\bigwedge \V^{(n)}\to CL({\cal V},Q) one has to transform to the standard construction. The injection is of course dependent on the antisymmetric part of the bilinear form. This process results in the appropriate vertex normalordering terms, which are now obtained from the theory itself and not added ad hoc via a regularization argument