Spinor states on a curved infinite disc with non-zero spin-connection fields

Abstract

In the paper of Lukman, Mankoc Borstnik, Nielsen (NJP 13 (2011) 103027) one step towards the realistic Kaluza-Klein[like] theories was made by presenting the case of a spinor in $d=(1+5)$ compactified on an (formally) infinite disc with the zweibein which makes a disc curved on an almost $S^2$ and with the spin connection field which allows on such a sphere only one massless spinor state of a particular charge, coupling the spinor chirally to the corresponding Kaluza-Klein gauge field. The solutions for the massless spinor state were found for a range of spin connection fields, as well as the massive ones for a particular choice of the spin connection field. In this paper we present the massless and massive spinor states for the whole range of parameters of the spin connection field, which allow only one massless solution.

21 pages, 8 figures, iopart style, some printing mistakes corrected and some explanations improved due to IOP referee suggestions

References in corpus (6)

• On the origin of families of fermions and their mass matrices
• "An effective two dimensionality" cases bring a new hope to the Kaluza-Klein[like] theories
• On the origin of families of quarks and leptons - predictions for four families
• Fermions with no fundamental charges call for extra dimensions
• An example of Kaluza-Klein-like theory with boundary conditions, which lead to massless and mass protected spinors chirally coupled to gauge fields
• Particular boundary condition ensures that a fermion in d=1+5, compactified on a finite disk, manifests in d=1+3 as massless spinor with a charge 1/2, mass protected and chirally coupled to the gauge field

Cited by in corpus (5)

• Can the spin-charge-family theory explain baryon number non conservation?
• Massless and massive representations in the spinor technique
• How does Clifford algebra show the way to the second quantized fermions with unified spins, charges and families, and with vector and scalar gauge fields beyond the {\it standard model}
• Spin-charge-family theory is offering next step in understanding elementary particles and fields and correspondingly universe
• A trial to understand the supersymmetry relations through extension of the second quantized fermion and boson fields, either to strings or to odd dimensional spaces