Covariance and Gauge Invariance in Continuum Physics : Application to Mechanics, Gravitation, and Electromagnetism / by Lalaonirina R. Rakotomanana.

Format:

Book

Author/Creator:

R. Rakotomanana, Lalaonirina, author.

Contributor:

SpringerLink (Online service)

Series:

Mathematics and Statistics (Springer-11649)

Progress in mathematical physics 1544-9998 ; 73.

Progress in Mathematical Physics, 1544-9998 ; 73

Language:

English

Subjects (All):

Mathematical physics.

Mechanics.

Mechanics, Applied.

Mathematical Physics.

Theoretical, Mathematical and Computational Physics.

Solid Mechanics.

Local Subjects:

Mathematical Physics.

Theoretical, Mathematical and Computational Physics.

Solid Mechanics.

Physical Description:

1 online resource (XI, 325 pages) : 42 illustrations, 16 illustrations in color.

Edition:

First edition 2018.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

978-3-319-91782-5

9783319917825

Access Restriction:

Restricted for use by site license.