A correspondence between standard model fermions and degrees of freedom of polycrystalline materials

TL;DR

This paper establishes a novel correspondence between the degrees of freedom in polycrystalline materials and the fermionic sector of the standard model, proposing a lattice-based framework that could underpin a unified theory of physics.

Contribution

It introduces a lattice Dirac operator on polycrystalline degrees of freedom, linking material science with fundamental particle physics, and suggests a new approach to unifying gravity and gauge fields.

Findings

Identifies affine transformations of grains with lattice fermionic degrees of freedom.

Defines a lattice Dirac operator matching the standard model's fermionic sector.

Proposes a lattice chiral symmetry similar to Ginsparg-Wilson.

Abstract

We identify natural degrees of freedom of polycrystalline materials -- affine transformations of grains -- with those of a three-dimensional lattice theory for $(T\otimes\Omega)(\mathbb{R}^3)$. We define a lattice Dirac operator on this space and identify its continuous limit with the free field limit of the whole fermionic sector of the standard model. Fermion doubling is used here as a tool to obtain the necessary number of steps of freedom. The correspondence extends to important structural properties (families, colors, flavor pairs, electromagnetic charge). We find a lattice version of chiral symmetry similar to the Ginsparg-Wilson approach. This correspondence suggests to propose a ``polycrystalline ether''. Combined with GLET, a general Lorentz ether theory of gravity with GR limit, this becomes a concept for a theory of everything. The extension to gauge fields is the major open problem and requires new concepts.