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Covariance and Gauge Invariance in Continuum Physics : Application to Mechanics, Gravitation, and Electromagnetism

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概要 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 cla...ssical 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.続きを見る
目次 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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本文を見る Full text available from Springer Mathematics and Statistics eBooks 2018 English/International

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登録日 2020.06.27
更新日 2020.06.28