Plasticity from Symmetry: A Gauge-Theoretic Framework

TL;DR

This paper develops a gauge-theoretic framework for plasticity, revealing it as a non-dissipative, symmetry-driven phenomenon with defect kinematics governed by gauge fields emerging from stress and defect conservation laws.

Contribution

It introduces a novel gauge-theoretic formulation of plasticity based on symmetry breaking and defect conservation, providing a fundamental, non-phenomenological description.

Findings

Plasticity can be described by a gauge theory derived from symmetry principles.

Dislocations and defects emerge as gauge charges with conservation laws.

Dissipative plastic flow is a controlled deformation of an underlying conservative gauge theory.

Abstract

Plastic deformation is widely regarded as an intrinsically dissipative phenomenon and its theoretical description is largely phenomenological. We argue instead that plasticity possesses a non-dissipative, symmetry determined backbone: defect kinematics are fixed by symmetry prior to dissipation and separate from constitutive assumptions. Starting from the spontaneous breaking of spacetime symmetries in a crystalline phase, we construct an effective field theory in which elasticity and geometry reorganize into a coupled higher-rank tensor vector gauge structure. The gauge fields are not postulated, rather they emerge naturally from stress and defect conservation laws. Dislocations, disclinations, and torsional defects appear as gauge charges of non-integrable geometry whose continuity equations and mobility constraints follow directly from Gauss laws. This clarifies the long-standing ambiguity over which variables are fundamental in the gauge theory of defects and shows that plasticity admits an ideal gauge-theoretic formulation, with dissipative flow arising as a controlled deformation of this conservative theory.