×

A null Berwald-Moor metric in nilpotent spinor space. (English) Zbl 1324.53031

Summary: Physics at its most fundamental level is concerned with the description of the fermion state. All experimental evidence to date implies that fermions are point-like singularities. Previous works on the quantum mechanics of fermions suggest that they require two space-like structures to generate the required algebra. Though these two spaces are dual, their combination involves symmetry-breaking, through the creation of five generators equivalent to the gamma matrices. The algebraic structure required for a fermion appears to be a nilpotent or square root of zero, and the spinor structure required to produce this has the form of a Berwald-Moor metric of zero magnitude. It is proposed that the creation of a fermion singularity of zero magnitude is only possible through the existence of two spaces, each dual to the other.

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
PDFBibTeX XMLCite