Group Invariant Solutions without Transversality and the Principle of Symmetric Criticality
Mathematical Physics
2009-10-31 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.math-ph/9910014,
title = {Group Invariant Solutions without Transversality and the Principle of Symmetric Criticality},
author = {I. Anderson and M. Fels and C. Torre},
journal= {arXiv preprint arXiv:math-ph/9910014},
year = {2009}
}
Comments
16 pages, AMSTeX, bugs fixed in example 3.2