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

Abstract

The genuine Kaluza-Klein-like theories--with no fields in addition to gravity--have difficulties with the existence of massless spinors after the compactification of some space dimensions \cite{witten}. We proposed in previous paper a boundary condition for spinors in d=(1+5) compactified on a flat disk that ensures masslessness of spinors (with all positive half integer charges) in d=(1+3) as well as their chiral coupling to the corresponding background gauge gravitational field. In this paper we study the same toy model, proposing a boundary condition allowing a massless spinor of one handedness and only one charge (1/2) and infinitely many massive spinors of the same charge, allowing disc to be curved. We define the operator of momentum to be Hermitean on the vector space of spinor states--the solutions on a disc with the boundary.

15 pages

References in corpus (5)

• How to generate families of spinors
• On the origin of families of fermions and their mass matrices
• Unification of Spins and Charges in Grassmann Space?
• 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

Cited by in corpus (5)

• "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
• Discrete symmetries in the Kaluza-Klein-like theories
• 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}
• Spinor states on a curved infinite disc with non-zero spin-connection fields