Symmetries and Hamiltonian formalism for complex materials

TL;DR

This paper explores the Hamiltonian structure and symmetries of multifield theories in complex materials, introducing Poisson brackets and Hamilton-Jacobi equations to advance the theoretical framework.

Contribution

It presents a novel Hamiltonian formalism for complex materials, incorporating Lie group invariance, Poisson brackets, and a spatial formulation without paragon assumptions.

Findings

Invariance under Lie group actions is established for substructural interactions.

Poisson brackets are formulated in the material representation.

A Hamilton-Jacobi equation for multifield models is derived.

Abstract

Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural interactions. Poisson brackets are also introduced in the material representation to account for general material substructures. A Hamilton-Jacobi equation suitable for multifield models is presented. Finally, a spatial version of all these topics is discussed without making use of the notion of paragon setting.