Comptes Rendus
no. 1-2
Is incompressible elasticity a conformal field theory?
[L'élasticité incompressible est-elle une théorie de champ conforme ?]
Markus Lazar1  ; Charalampos Anastassiadis1
1 Emmy Noether Research Group, Department of Physics, Darmstadt University of Technology, Hochschulstr. 6, 64289 Darmstadt, Germany
Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 163-169.

Dans ce travail, nous examinons la théorie de l'élasticité linéaire incompressible isotrope en tant que théorie conforme. Nous calculons les courants conformes, les lois de conservation et les lois de bilan de l'élasticité incompressible. Nous examinons les symétries d'Euler–Lagrange, ainsi que les symétries variationnelles et les symétries de divergence. Si la pression est nulle, le groupe conforme est le groupe de symétrie pour l'élasticité homogène linéaire isotrope incompressible en l'absence de forces extérieures. La symétrie additionnelle est la transformation spéciale conforme. Nous discutons aussi les termes des transformations spéciales conformes de l'élasticité qui brisent la symétrie.

In this work, we investigate the theory of linear isotropic incompressible elasticity as a conformal field theory. We calculate the conformal currents, the conservation laws and the balance laws of incompressible elasticity. We investigate the Euler–Lagrange symmetries, variational and divergence symmetries. If the pressure p=0, the conformal group is the symmetry group for homogeneous isotropic linear incompressible elasticity without external forces. The additional symmetry is the special conformal transformation. We also discuss the symmetry breaking terms of special conformal transformations in elasticity.

Publié le :
DOI : 10.1016/j.crme.2007.11.006
Keywords: Incompressible elasticity, Conservation laws, Eshelby stress tensor, Conformal field theory
Mot clés : Élasticité incompressible, Lois de conservation, Tenseur des contraintes d'Eshelby, Théorie de champ conforme
Markus Lazar 1 ; Charalampos Anastassiadis 1

1 Emmy Noether Research Group, Department of Physics, Darmstadt University of Technology, Hochschulstr. 6, 64289 Darmstadt, Germany 
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Markus Lazar; Charalampos Anastassiadis. Is incompressible elasticity a conformal field theory?. Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 163-169. doi : 10.1016/j.crme.2007.11.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.11.006/

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