Covariance and Gauge Invariance in Continuum Physics

Application to Mechanics, Gravitation, and Electromagnetism

  • Lalaonirina R. Rakotomanana

Part of the Progress in Mathematical Physics book series (PMP, volume 73)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Lalaonirina R. Rakotomanana
    Pages 1-8
  3. Lalaonirina R. Rakotomanana
    Pages 73-93
  4. Lalaonirina R. Rakotomanana
    Pages 95-175
  5. Lalaonirina R. Rakotomanana
    Pages 177-238
  6. Lalaonirina R. Rakotomanana
    Pages 239-300
  7. Lalaonirina R. Rakotomanana
    Pages 301-302
  8. Back Matter
    Pages 303-325

About this book


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.


covariant lagrangian gauge invariance riemann-cartan geometry continuum mechanics gravitation electromagnetism heterogeneous wave propagation

Authors and affiliations

  • Lalaonirina R. Rakotomanana
    • 1
  1. 1.Institut de Recherche MathématiqueUniversité de RennesRennes CXFrance

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