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A Relativistic Gauge Theory of Nonlinear Quantum Mechanics and Newtonian Gravity

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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 Schrödinger picture of a given field theory. While, for simplicity, we study the example of a \(\mathcal{U}(1)\) 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 Schrödinger-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.

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  1. Dipartimento di Fisica, Università di Pisa, Largo Pontecorvo 3, 56127, Pisa, Italy

    Hans-Thomas Elze

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  1. Hans-Thomas Elze
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Correspondence to Hans-Thomas Elze.

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Elze, HT. A Relativistic Gauge Theory of Nonlinear Quantum Mechanics and Newtonian Gravity. Int J Theor Phys 47, 455–467 (2008). https://doi.org/10.1007/s10773-007-9471-6

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  • DOI: https://doi.org/10.1007/s10773-007-9471-6

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