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arXiv · 0704.2683

A relativistic gauge theory of nonlinear quantum mechanics and Newtonian gravity

Hans-Thomas Elze
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Abstract

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 a 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, similar to recently studied Schroedinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. A probabilistic interpretation (Born's rule) holds, provided the underlying model is scale free. Keywords: nonlinear functional Schroedinger equation, gauge symmetry, Newtonian gravity.

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Hans-Thomas Elze. 2007-04-20. A relativistic gauge theory of nonlinear quantum mechanics and Newtonian gravity. https://doi.org/10.1007/s10773-007-9471-6

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