Illustrations of the Becchi-Rouet-Stora-Tyutin invariance by means of simple toy models

Among the available quantization methods for gauge field theories, the Becchi-Rouet-StoraTyutin ͑BRST͒ procedure has emerged as the simplest one for non-Abelian field theories, and thus the one that is systematically used in such cases. Our aim is to provide the reader with an accessible introduction to this modern and elegant treatment of constrained systems through its application to two simple mechanical models: a particle moving on a ring, and a particle on the surface of a sphere. If the description of these models is made from a moving frame of reference, they constitute simple analogs of gauge field theories. Notwithstanding their simplicity, these two applications display the main features of the BRST method, dealing with Abelian and non-Abelian symmetries, respectively. They also illustrate the solution of many-body problems in which broken symmetries are restored by means of collective coordinates describing the motion of the moving frame. Both the Hamiltonian and the Lagrangian formulations are presented, the latter using the antifield formalism