Physics – Quantum Physics
Scientific paper
2000-02-02
Physics
Quantum Physics
Submitted Jan. 2000 for the Procs. of the International Symposium `Quantum Theory and Symmetries' (Goslar, 18-22 July 1999). E
Scientific paper
An enlarged group G of nonlinear transformations, modeled on the general linear group GL(2,R), leads to a beautiful, apparently unremarked symmetry between the wave function's phase and the logarithm of its amplitude. Equations Doebner and I earlier proposed are embedded in a wider, natural family of nonlinear time-evolution equations, on which G acts as a gauge group (leaving physical observations invariant). There exist G-invariant quantities that reduce to the usual probability density and flux for linearizable quantum theories in a particular gauge.
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