Conformally dual fields in relativistic classical and quantum mechanics

The conditions governing the existence of conformally dual scalar fields in both classical and quantum theories are derived. The transformation properties of the Hamilton-Jacobi and Klein-Gordon equations under conformal mappings are established and utilized as the basis for the analysis. The existence of self-dual fields is demonstrated and examples are presented. Previously known results applicable to the Schrodinger equation and to Newtonian mechanics are shown to follow in the nonrelativistic limit as special cases of the present study. (C) 1996 American Association of Physics Teachers.