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

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Lalaonirina R. Rakotomanana

Covariance and Gauge Invariance in Continuum Physics

Application to Mechanics, Gravitation, and Electromagnetism

Lalaonirina R. Rakotomanana

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English

Birkhauser Verlag AG
12 July 2018

Mathematical physics; Mechanical engineering & materials

Series: Progress in Mathematical Physics

Summary
Details

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.

By: Lalaonirina R. Rakotomanana
Imprint: Birkhauser Verlag AG
Country of Publication: Switzerland
Edition: 2018 ed.
Volume: 73
Dimensions: Height: 235mm, Width: 155mm,
Weight: 676g
ISBN: 9783319917818
ISBN 10: 3319917811
Series: Progress in Mathematical Physics
Pages: 325
Publication Date: 12 July 2018
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active