All Physics Faculty Publications

Group Invariant Solutions without Transversality and the Principle of Symmetric Criticality

Ian M. Anderson, Utah State University
Mark E. Fels, Utah State University
Charles G. Torre, Utah State University


We extend Lie's classical method for finding group invariant solutions to the case of non-transverse group actions. For this extension of Lie's method we identify a local obstruction to the principle of symmetric criticality. Two examples of non-transverse symmetry reductions for the potential form of Maxwell's equations are then examined.