Nonlinear quantum mechanics: Results and open questions

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Abstract

About 15 years ago, we (Heinz-Dietrich Doebner and I) proposed a special type of nonlinear modification of the usual Schrödinger time-evolution equation in quantum mechanics. Our equation was motivated by certain unitary representations of the group of diffeomorphisms of physical space, in the framework of either nonrelativistic local current algebra or quantum Borel kinematics. Subsequently, we developed this and related approaches to nonlinearity in quantum mechanics considerably further, to incorporate theories of measurement, groups of nonlinear gauge transformations, symmetry and invariance properties, unification of a large family of nonlinear perturbations, and possible physical contexts for quantum nonlinearity. Some of our results and highlights of some open questions are summarized.

Original languageEnglish (US)
Pages (from-to)884-891
Number of pages8
JournalPhysics of Atomic Nuclei
Volume71
Issue number5
DOIs
StatePublished - May 1 2008

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics

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