Perspectives on Nonlinearity in Quantum Theory
摘要
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.
引用
@article{arxiv.quant-ph/0002013,
title = {Perspectives on Nonlinearity in Quantum Theory},
author = {Gerald A. Goldin},
journal= {arXiv preprint arXiv:quant-ph/0002013},
year = {2007}
}
备注
Submitted Jan. 2000 for the Procs. of the International Symposium `Quantum Theory and Symmetries' (Goslar, 18-22 July 1999). Eds. H.-D. Doebner, V. K. Dobrev, J.-D. Hennig and W. Luecke. Singapore: World Scientific (in press)