A complete basis set of functionally independent invariants of continuous Lie groups

Abstract

Using the methods of differential equations the author has obtained the complete set of functionally independent bases of invariants for some continuous Lie groups of mathematical physics: (i) the conformal group; (ii) the semi-direct product of the Weyl group and the one-parameter group of Psi translation; (iii) the direct product of the Poincare group and the one parameter group of Psi scaling; (iv) the Weyl group; (v) the 14-parameter maximal symmetry group of the Schrodinger equation for the Coulombic system of atoms and molecules; and (vi) SU(3) of elementary particle physics. the first four groups are the only groups which, together with the Poincare group, are the maximal symmetry groups of all forms of the non-linear Klein-Gordon equation.