31 research outputs found
A condensed matter interpretation of SM fermions and gauge fields
We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on
it, as a three-dimensional geometric interpretation of the SM fermions. Each C
x /(R^3) describes an electroweak doublet. The Dirac equation has a
doubler-free staggered spatial discretization on the lattice space Aff(3) x C
(Z^3). This space allows a simple physical interpretation as a phase space of a
lattice of cells in R^3. We find the SM SU(3)_c x SU(2)_L x U(1)_Y action on
Aff(3) x C x /(R^3) to be a maximal anomaly-free special gauge action
preserving E(3) symmetry and symplectic structure, which can be constructed
using two simple types of gauge-like lattice fields: Wilson gauge fields and
correction terms for lattice deformations. The lattice fermion fields we
propose to quantize as low energy states of a canonical quantum theory with
Z_2-degenerated vacuum state. We construct anticommuting fermion operators for
the resulting Z_2-valued (spin) field theory. A metric theory of gravity
compatible with this model is presented too.Comment: Minimal modifications in comparison with the published versio