INTRODUCING NONLINEAR GAUGE TRANSFORMATIONS IN A FAMILY OF NONLINEAR SCHRODINGER-EQUATIONS

In earlier work we proposed a family of nonlinear time-evolution equat ions for quantum mechanics associated with certain unitary group repre sentations [Doebner and Goldin, Phys. Lett. A 162, 397 (1992); J. Phys . A 27, 1771 (1994)]. Such nonlinear Schrodinger equations are expecte d to describe irreversible and dissipative quantum systems. Here we in troduce and justify physically the group of nonlinear gauge transforma tions necessary to interpret our equations. We determine the parameter s that are actually gauge invariant and describe some of their propert ies. Our conclusions contradict, at least in part, the view that any n onlinearity in quantum mechanics leads to unphysical predictions. We a lso show how time-dependent nonlinear gauge transformations connect ou r equations to those proposed by Kostin [J. Chem. Phys. 57, 3589 (1972 )] and by Bialynicki-Birula and Mycielski [AM. Phys. 100, 62 (1976)]. We believe our approach to be a fundamental generalization of the usua l notions about gauge transformations in quantum mechanics.