A condensed matter interpretation of SM fermions and gauge fields
Schmelzer, I.
Original · EN
We present the bundle Aff(3) x C x /(R³), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each C x /(R³) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space Aff(3) x C (Z³). This space allows a simple physical interpretation as a phase space of a lattice of cells in R³. We find the SM SU(3)c x SU(2)ₗ x U(1)Y action on Aff(3) x C x /(R³) 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 Z₂-degenerated vacuum state. We construct anticommuting fermion operators for the resulting Z₂-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.
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