The Standard Model fermions as excitations of an ether

Abstract

The three-dimensional complexified exteriour bundle $C \otimes \Lambda(R^3)$ is proposed as a geometric interpretation of electroweak doublets of Dirac fermions. The Dirac equation on this bundle allows a staggered discretization on a three-dimensional scalar complex lattice field $C(Z^3)$. The three-dimensional affine group $Aff(3)$ is proposed as a geometric interpretation for the matrix defined by the three generations, with the three quark doublets and a lepton doublet in each generation. The corresponding lattice space $(Aff(3) \otimes C)(Z^3)$ allows a simple condensed matter (ether) interpretation. A possibility to construct anticommuting fermion operators based on canonical quantization is given. A set of axioms of the gauge action is defined such that the gauge action of the SM gauge group $SU(3)_c x SU(2)_L x U(1)_{Y}$ is the maximal possible one. This includes preservation of Euclidean symmetry and the symplectic structure, anomaly freedom, ground state neutrality, and the possibility of realization on the lattice. Strong interactions are realized as Wilson-like gauge fields, weak gauge fields as effective gauge fields describing lattice deformations, and the EM field as a combination of above types. Some possibilities to explain the qualitative characteristics of the mass parameters are discussed.