Dirac-bracket quantisation of a constrained nonlinear system: the rigid rotator

The Dirac-bracket quantisation procedure for the nonrelativistic rigid rotator is discussed. In cartesian coordinates this system exhibits two important features which are also characteristic of the nonabelian gauge theories, it it constrained, and nonlinear. By comparing to the known solution in polar coordinates it is demonstrated that simple hermiticity conditions are sufficient to allow the unambiguous applications of the Dirac quantisation method to such nonlinear dynamical systems. (author)