On duality between Cosserat elasticity and fractons
Andrey Gromov, Piotr Surowka
Abstract
We present a dual formulation of the Cosserat theory of elasticity. In this theory a local element of an elastic body is described in terms of local displacement and local orientation. Upon the duality transformation these degrees of freedom map onto a coupled theory of a U(1) vector-valued one-form gauge field and an ordinary U(1) gauge field. We discuss the degrees of freedom in the corresponding gauge theories, relation to symmetric tensor gauge theories, the defect matter and coupling to the curved space.
Topics & Concepts
Duality (order theory)MathematicsGauge theoryElasticity (physics)Tensor fieldGauge (firearms)Classical mechanicsDegrees of freedom (physics and chemistry)PhysicsTensor (intrinsic definition)S-dualityCoupling (piping)Theoretical physicsMathematical analysisField theory (psychology)Field (mathematics)Displacement fieldMathematical physicsDual (grammatical number)Introduction to gauge theoryDisplacement (psychology)Element (criminal law)Transformation (genetics)Gauge fixingFiber bundleLinear elasticityNonlocal and gradient elasticity in micro/nano structuresComposite Material MechanicsThermoelastic and Magnetoelastic Phenomena