Is there a relativistic nonlinear generalization of quantum mechanics?

Details Is there a relativistic nonlinear generalization of quantum mechanics? Is there a relativistic nonlinear generalization of quantum mechanics?

2007-04-19

arxiv.org/abs/0704.2559v1

J.Phys.Conf.Ser.67:012016,2007

Physics

Quantum Physics

10 pages; talk at DICE 2006 (Piombino, September 11-15, 2006); to appear in Journal of Physics: Conference Series (2007)

Scientific paper

10.1088/1742-6596/67/1/012016

Yes, there is. - A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for simplicity, we study the example of an U(1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, where it leads to the Schroedinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. The probabilistic interpretation, i.e. Born's rule, holds provided the underlying model has only dimensionless parameters.

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