Quantum Gravity and String Theory


On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy

Authors: Carlos Castro

A novel (to our knowledge) Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson's fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final formulation of Quantum Gravity.

Comments: 18 pages, has been submitted to Foundations of Physics

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Submission history

[v1] 8 Mar 2010
[v2] 11 Apr 2010

Unique-IP document downloads: 699 times

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