Transformation-Theoretic Problems in Variant Field Theory. II: Lagrangian Classes Admitting an R-Parameter Invariance Group

摘要

This Memorandum presents a study of the most general Lagrangian functions for which the field equations of variant field theory are such that the geometric object fields comprising the dependent variable set are invariant under a finite continuous group of coordinate transformations. The arguments are based on the concept of a geometry class. This enables the results to be cast in as general a context as possible yet allowing the derivation of specific systems of partial differential equations whose solution manifolds span the class of admissible Lagrangian functions. (Author)