Structure of nonlinear gauge transformations
Marek Czachor
Abstract
Nonlinear Doebner-Goldin [Phys. Rev. A 54, 3764 (1996)] gauge transformations (NGT) defined in terms of a wave function ψ(x) do not form a group. To get a group property one has to consider transformations that act differently on different branches of the complex argument function and the knowledge of the value of ψ(x) is not sufficient for a well defined NGT. NGT that are well defined in terms of ψ(x) form a semigroup parametrized by a real number γ and a nonzero λ which is either an integer or -1≤ λ≤ 1. An extension of NGT to projectors and general density matrices leads to NGT with complex γ. Both linearity of evolution and Hermiticity of density matrices are gauge dependent properties.
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