Linear Quantum Theory and Its Possible Nonlinear Generalizations

✍ Scribed by K.R.W. Jones

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 904 KB
• Volume: 233
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1994.1070

✦ Synopsis

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. 1994 Academic Press, Inc.