Covariance and Gauge Invariance in Continuum Physics

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 Poincar� 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.

Aceasta carte prezinta un model de abordare lagrangiana pentru a formula diverse domenii ale fizicii continuumului, variind de la elasticitatea continuumului gradient pana la gravito-electromagnetismul relativist. Extinde teoriile clasice bazate pe geometria Riemann la geometria Riemann-Cartan, apoi descrie continuum neomogen si spatiu-timp cu torsiune in gravitatia relativista Einstein-Cartan. Investigeaza doua aspecte ale invariantei Lagrangianului: covarianta formularii urmand metoda Lovelock si Rund si invarianta gabaritului in care se considera invarianta difeomorfismului activ prin utilizarea teoriei gabaritului Poincar local conform metodei Utiyama. Mai mult, dezvolta diferite extensii ale elasticitatii continuumului gradientului de deformare, gravitatiei relativiste si electromagnetismului atunci cand campul de torsiune al Riemann -Continuul cartan nu este egal cu zero.