Overview
- Presents a Lagrangian approach model to formulate various fields of continuum physics
- Extends the classical theories based on Riemann geometry to Riemann-Cartan geometry
- Describes non-homogeneous continuum and spacetime with torsion in Einstein-Cartan relativistic gravitation
Part of the book series: Progress in Mathematical Physics (PMP, volume 73)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Covariance and Gauge Invariance in Continuum Physics
Book Subtitle: Application to Mechanics, Gravitation, and Electromagnetism
Authors: Lalaonirina R. Rakotomanana
Series Title: Progress in Mathematical Physics
DOI: https://doi.org/10.1007/978-3-319-91782-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-91781-8Published: 12 July 2018
Softcover ISBN: 978-3-030-06298-9Published: 20 December 2018
eBook ISBN: 978-3-319-91782-5Published: 04 July 2018
Series ISSN: 1544-9998
Series E-ISSN: 2197-1846
Edition Number: 1
Number of Pages: XI, 325
Number of Illustrations: 26 b/w illustrations, 16 illustrations in colour
Topics: Mathematical Physics, Theoretical, Mathematical and Computational Physics, Solid Mechanics