A relativistic gauge theory of nonlinear quantum mechanics and Newtonian gravity

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.

16 pages; to appear in Int. J. Theor. Phys. (2007)

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Cited by in corpus (2)

• The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata
• Geometric Interpretation of a nonlinear extension of Quantum Mechanics