01841cam a22002295i 4500 38349 38349 180704s2018 gw |||| o |||| 0|eng 9783030062989 Rakotomanana, RLalaonirina, Covariance and Gauge Invariance in Continuum Physics : Application to Mechanics, Gravitation, and Electromagnetism / by Lalaonirina R. Rakotomanana. . Switzerland Birkhauser 2020 xi, 325 p.; ill.; 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. Mathematical physics. 2291 Mechanics, Applied. 2191 Mechanics. 5130 Mathematical Physics. 2291 Solid Mechanics. Theoretical, Mathematical and Computational Physics. BK 0 0 lcc 0 0 MAIN MAIN OOWR 2024-05-08 GFT 0 QC173.7 .R35 2020 00048541 2024-05-08 00:00:00 2024-05-08 BK