Possibility of Geometric Description of Quasiparticles in Solids

TL;DR

This paper proposes a novel geometric framework for describing quasiparticles in solids by modeling the crystal as an anisotropic space-time with a specific metric, leading to relativistic-like wave equations for collective excitations.

Contribution

It introduces a new phenomenological approach that models quasiparticles using relativistic wave equations within a geometric space-time framework tailored for crystalline materials.

Findings

Derivation of generalized Klein-Gordon-Fock and Dirac equations in the crystal context

Application discussion to conduction electrons in solids

Potential for a unified geometric description of quasiparticles

Abstract

New phenomenological approach for the description of elementary collective excitations is proposed. The crystal is considered to be an anisotropic space-time vacuum with a prescribed metric tensor in which the information on electromagnetic crystalline fields is included. The quasiparticles in this space are supposed to be described by the equations structurally similar to the relativistic wave equations for particles in empty space. The generalized Klein-Gordon-Fock equation and the generalized Dirac equation in external electromagnetic field are considered. The applicability of the proposed approach to the case of conduction electron in a crystal is discussed.