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＜電子ブック＞
Covariance and Gauge Invariance in Continuum Physics : Application to Mechanics, Gravitation, and Electromagnetism / by Lalaonirina R. Rakotomanana
(Progress in Mathematical Physics. ISSN:21971846 ; 73)

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Birkhäuser)
出版年	2018
大きさ	XI, 325 p. 42 illus., 16 illus. in color : online resource
著者標目	*R. Rakotomanana, Lalaonirina author SpringerLink (Online service)
件　名	LCSH:Mathematical physics LCSH:Mechanics, Applied LCSH:Solids FREE:Mathematical Physics FREE:Theoretical, Mathematical and Computational Physics FREE:Solid Mechanics
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-91782-5

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