Orbit Spaces in Superconductivity

In the framework of Landau theory of phase transitions one is interested to describe all the possible low symmetry ``superconducting'' phases allowed for a given superconductor crystal and to determine the conditions under which this crystal undergoes a phase transition. These problems are best described and analyzed in the orbit space of the high symmetry group of the ``normal, non-superconducting'' phase of the crystal. In this article it is worked out a simple example concerning superconductivity, that shows the P-matrix method to determine the equations and inequalities defining the orbit space and its stratification. This approach is of general validity and can be used in all physical problems that make use of invariant functions, as long as the symmetry group is compact.