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Field of complex linear frames on real space-time manifold as dynamical variable for generally-covariant models

Godlewski P.

Demonstratio Mathematica

2005

Vol. 38, nr 4

819--835

A model of the self-interacting field of complex linear frames E on an n-dimensional real manifold is investigated. The model is generally-covariant and GL(n, C)- invariant. If n = 4, the components of E can be interpreted as dynamical variables for the gravitational field. A Lagrangian of E is constructed, the Euler-Lagrange equations are derived and a wide class of their solutions is found. The solutions are built of left invariant vector fields on a real semisimple Lie group "deformed" by a complex factor of a natural exponential structure.