Families of spinors in $d=(1+5)$ with zweibein and two kinds of spin connection fields on an almost $S^2$

Abstract

We studied (arxiv: 1001.4679, 1205.1714) properties of spinors in a toy model in $d=(1+5)$ as a step towards realistic Kaluza-Klein (like) theories in non compact spaces. ${\mathcal{M}}^{(5+1)}$ was assumed to break to an infinite disc with a zweibein which makes a disc curved on $S^2$ and with a spin connection field which allows on such a sphere only one massless spinor state. This time we are taking into account families of spinors interacting with several spin connection fields, as required for this toy model by the spin-charge-family theory We are studying possible masslesness of families of spinors: Spinors regroup into subgroups of an even number of families.

10 pages, To appear in the Proceedings to the 15th Bled Workshop "What Comes Beyond Standard Models", DMFA ZALOZNISTVO, December 2012, Vol. 13, No. 2

References in corpus (1)

• "An effective two dimensionality" cases bring a new hope to the Kaluza-Klein[like] theories