Covariance and Gauge Invariance in Continuum Physics: Application to Mechanics, Gravitation, and Electromagnetism

by Lalaonirina R. Rakotomanana

Overview

This book presents a Lagrangian approach model to formulate various fields of continuum physics, ranging from gradient continuum elasticity to relativistic gravito-electromagnetism. It extends the classical theories based on Riemann geometry to Riemann-Cartan geometry, and then describes non-homogeneous continuum and spacetime with torsion in Einstein-Cartan relativistic gravitation.

It investigates two aspects of invariance of the Lagrangian: covariance of formulation following the method of Lovelock and Rund, and gauge invariance where the active diffeomorphism invariance is considered by using local Poincaré gauge theory according to the Utiyama method.

Further, it develops various extensions of strain gradient continuum elasticity, relativistic gravitation and electromagnetism when the torsion field of the Riemann-Cartan continuum is not equal to zero. Lastly, it derives heterogeneous wave propagation equations within twisted and curved manifolds and proposes a relation between electromagnetic potential and torsion tensor.

Product Details

ISBN-13:	9783030062989
Publisher:	Springer International Publishing
Publication date:	12/19/2018
Series:	Progress in Mathematical Physics , #73
Edition description:	Softcover reprint of the original 1st ed. 2018
Pages:	325
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

General introduction.- Basic concepts on manifolds, spacetimes, and calculus of variations.- Covariance of Lagrangian density function.- Gauge invariance for gravitation and gradient continuum.- Topics in continuum mechanics and gravitation.- Topics in gravitation and electromagnetism.- General conclusion.- Annexes