Quasi-Abelian gauge theory of axisymmetric deformation of shells of revolution

Abstract

We call attention to the possibility of constructing the gauge field theory for the classical continuum mechanics. As an example, we show that the Reissner's equations of axisymmetric deformation of shells of revolution have the geometric structure of pure (2 + time)-dimensional gauge continuum with Abelian T(2) ▶ SO(2) symmetry group. An essential element of this paper is the identification of several basic objects of gauge theory, such as the pure gauge potential, the strength field tensor and the Yang-Mills equations with basic elements of the Reissner's shell equations.