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Covariance and gauge invariance in C...

Rakotomanana, Lalaonirina R.

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

Record Type:	Electronic resources : Monograph/item
Title/Author:	Covariance and gauge invariance in Continuum Physics/ by Lalaonirina R. Rakotomanana.
Reminder of title:	application to mechanics, gravitation, and electromagnetism /
Author:	Rakotomanana, Lalaonirina R.
Published:	Cham :Springer International Publishing : : 2018.,
Description:	xi, 325 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Field theory (Physics) -
Online resource:	http://dx.doi.org/10.1007/978-3-319-91782-5
ISBN:	9783319917825

Covariance and gauge invariance in Continuum Physics = application to mechanics, gravitation, and electromagnetism /
Rakotomanana, Lalaonirina R.

Covariance and gauge invariance in Continuum Physicsapplication to mechanics, gravitation, and electromagnetism /[electronic resource] :by Lalaonirina R. Rakotomanana. - Cham :Springer International Publishing :2018. - xi, 325 p. :ill., digital ;24 cm. - Progress in mathematical physics,v.731544-9998 ;. - Progress in mathematical physics ;v.73..

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 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.

ISBN: 9783319917825

Standard No.: 10.1007/978-3-319-91782-5doiSubjects--Topical Terms:

707053
Field theory (Physics)

LC Class. No.: QC173.7 / .R356 2018

Dewey Class. No.: 530.14

Covariance and gauge invariance in Continuum Physics = application to mechanics, gravitation, and electromagnetism /
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245 1 0 $a Covariance and gauge invariance in Continuum Physics $h [electronic resource] : $b application to mechanics, gravitation, and electromagnetism / $c by Lalaonirina R. Rakotomanana.
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300 $a xi, 325 p. : $b ill., digital ; $c 24 cm.
490 1 $a Progress in mathematical physics, $x 1544-9998 ; $v v.73
505 0 $a 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.
520 $a 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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