Covariance and Gauge Invariance in Continuum Physics

Application to Mechanics, Gravitation, and Electromagnetism
1. Auflage 2018
ISBN: 978-3-319-91781-8
Verlag: Springer International Publishing

Buch, Englisch, Band 73, 325 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 676 g

Reihe: Progress in Mathematical Physics

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.

Zielgruppe

Research

Autoren/Hrsg.

R. Rakotomanana, Lalaonirina

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Kontinuumsmechanik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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