Linear Quantum Theory and Its Possible Nonlinear Generalizations

Jones K.R.W. (1994) Linear Quantum Theory and Its Possible Nonlinear Generalizations. Annals of Physics, 233 2: 295-316. doi:10.1006/aphy.1994.1070

Author Jones K.R.W.
Title Linear Quantum Theory and Its Possible Nonlinear Generalizations
Journal name Annals of Physics   Check publisher's open access policy
ISSN 0003-4916
Publication date 1994-08-01
Sub-type Article (original research)
DOI 10.1006/aphy.1994.1070
Volume 233
Issue 2
Start page 295
End page 316
Total pages 22
Language eng
Subject 3100 Physics and Astronomy
Abstract We show that the Schrödinger equation may be derived as a consequence of three postulates: 1) the hamiltonian formalism 2) a conformal structure 3) a projective structure. These suffice to deduce the geometrical structure of Hilbert space also. Furthermore, the quantum mechanical action principle, and unitary propagator, are reduced to special cases of classical results. Thereafter we explore the relaxation of these postulates. Of the possible generalizations only one appears physically fruitful. This is obtained from a simple gauge freedom of the standard theory. The result is a nonlinear quantum theory that has been the subject of recent interest. We consider the empirical status of this theory, and the problem of its interpretation. It is suggested that the only remaining option is to consider nonperturbative nonlinearities in the context of the quantum measurement problem. This is advanced as a principle of constraint.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
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Citation counts: Scopus Citation Count Cited 4 times in Scopus Article | Citations
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Created: Tue, 14 Jun 2016, 16:39:11 EST by System User