Tetrad, connection, and metric as independent variables in lagrangians of micromorphic continua models

Abstract

In continuous media theory, models with a tetrad, a metric, or a connection field as the independent variable are widely used. Unification of these formalisms is presented. Models with a Lagrangian dependent on tetrad, connection, and metric fields treated as independent variables are investigated. The tetrad and the connection play the role of dynamic variables, but the metric is a nondynamic one. This means there are no derivatives of the metric in the Lagrangian. In a Polyakov-like way, as in string theory, the metric is eliminated from the Lagrangian and field equations. The Lagrangian takes a simple square-root form as the Nambu Lagrangian. It connects in a sense Lagrangians from theGl(n, R)-invariant and Kijowski theories. The distinguished solutions, for a symmetric connection are semisimple Lie groups. The model gives the possibility of simultaneous description of fields of different natures and can be applied in the description of continuous media with complicated internal structure and in external fields.