Abstract
The authors develop a method for calculating the Cartan forms in the parametrization of group transformations which has a simple composition law and satisfies the condition called the naturalness. The method is applied to gauge theories for finding the explicit transformation laws of gauge fields under finite local transformations of groups, and to chiral field theories for setting up chiral field Lagrangians. The explicit forms of finite transformations of gauge fields and their nonlinear realizations for gravity and supergravity are found. The expressions of the Cartan forms, the Lagrangians of the principal chiral fields and the Goldstone fields for the unitary groups U(2), SU(2), U(3), SU(3) and the coset spaces associated with these groups are derived. The Lagrangians obtained are distinguished from the previous known ones by new types of nonlinearity.
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