A condensed matter interpretation of the Standard Model

Condensed matter physics provides mathematical analogies with particle physics. Quasiparticles, i.e. particle-like excitations of a given ground state, often share many physical properties with more fundamental particles. Among the many attempts to find deeper insights into the Standard Model is the exportation of analogies in the other direction: from condensed-matter physics to fundamental physics. Here’s one such line of work:

I. Schmelzer. A condensed matter interpretation of SM fermions and gauge fields. arXiv:0908.0591

Abstract: 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.

A recent follow up paper focuses on neutrinos:

I. Schmelzer. Neutrinos as pseudo-acoustic ether phonons. arXiv:0912.3892

Abstract: Recently [arXiv:0908.0591] the author has proposed a condensed matter model which gives all fermions and gauge fields of the standard model of particle physics. In the model, the inertness of right-handed neutrinos is explained by an association with translational symmetry. We argue that this association may be used as well to explain the small neutrino masses. They appear to be pseudo-Goldstone particles associated with an approximate translational symmetry of a subsystem. Then we propose to explain the masslessness of SU(3)_c x U(1)_em with an unbroken SU(3)x U(1) gauge symmetry of the model. We also detect a violation of a necessary symmetry property in the lattice Dirac equation and present a fix for this problem.

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