Covariance and gauge invariance in Continuum Physics : application to mechanics, gravitation, and electromagnetism

• 作者： Rakotomanana, Lalaonirina R., author.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Progress in mathematical physics ;
• 出版： Cham : Springer International Publishing :Imprint: Birkhauser
• 叢書名： Progress in mathematical physics,volume 73
• 主題： Field theory (Physics) , Analysis of covariance. , Gauge invariance. , Mathematics. , Mathematical Physics. , Theoretical, Mathematical and Computational Physics. , Continuum Mechanics and Mechanics of Materials.
• ISBN： 9783319917825 (electronic bk.) 、 9783319917818 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
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• 摘要註: 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 Poincare 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.
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