Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Fundamental theories of physics

Quantum Theory from a Nonlinear Perspective

Dieter Schuch

Published Jan 1, 2018• 39 citations
Publisher
DOI
10.1007/978-3-319-65594-9

Related papers

Foundations of Nonlinear Quantum Physics

J. R. Croca

Quantum Matter•Jun 1, 2015•0 citations

Quantum Theory from a Nonlinear Perspective: Riccati Equations in Fundamental Physics

Dieter Schuch

•Jan 30, 2018•17 citations

Perspectives on Nonlinearity in Quantum Theory

Gerald A. Goldin

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.

arXiv:quant-ph/0002013•Feb 2, 2000•4 citations

Perspectives in quantum theory

Wolfgang Yourgrau, Alwyn van der Merwe, Alfred Landé

Dover Publications eBooks•Jan 1, 1971•247 citations

Quantum Theory and Beyond

Ted Bastin

•Jul 1, 2009•58 citations

Supersymmetry and nonlinear filtering: operator perspective

Bhashyam Balaji

Supersymmetry (SUSY), or Bose-Fermi symmetry, is an attempt to provide a unified description of all of the fundamental interactions. Although originally introduced in the quantum field theory context, it was noted by Witten that the understanding of certain features of SUSY was simpler in the quantum mechanical setting. Some aspects of the vast subject of supersymmetric quantum mechanics, and the supersymmetric Fokker-Planck equation, of relavance to continuous-time nonlinear filtering theory are briefly reviewed. The applicability of certain remarkable results in supersymmetric quantum mechanics to nonlinear filtering is noted and illustrated with a few examples.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 20, 2014•1 citation
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.
Supersymmetry (SUSY), or Bose-Fermi symmetry, is an attempt to provide a unified description of all of the fundamental interactions. Although originally introduced in the quantum field theory context, it was noted by Witten that the understanding of certain features of SUSY was simpler in the quantum mechanical setting. Some aspects of the vast subject of supersymmetric quantum mechanics, and the supersymmetric Fokker-Planck equation, of relavance to continuous-time nonlinear filtering theory are briefly reviewed. The applicability of certain remarkable results in supersymmetric quantum mechanics to nonlinear filtering is noted and illustrated with a few examples.