A Condensed Matter Interpretation of SM Fermions and Gauge Fields
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- Schmelzer, I. Found Phys (2009) 39: 73. doi:10.1007/s10701-008-9262-9
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We present the bundle (Aff(3)⊗ℂ⊗Λ)(ℝ3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (ℂ⊗Λ)(ℝ3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space (Aff(3)⊗ℂ)(ℤ3). This space allows a simple physical interpretation as a phase space of a lattice of cells.
We find the SM SU(3)c×SU(2)L×U(1)Y action on (Aff(3)⊗ℂ⊗Λ)(ℝ3) to be a maximal anomaly-free 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.