Hi The wish and desire of having physics independent of coordinate system can not be met nor fulfilled. The Madelung constant is proof of this. It becomes divergent in spherical coordinates and convergent in cubic coordinate. Covariance can thus be forgotten.
Check http://en.wikipedia.org/wiki/Madelung_constant Are there any other examples of this effect where choice of coordinate system gives different values? David David Jonsson, Sweden, phone callto:+46703000370