On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy
نویسنده
چکیده
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. PACS numbers: 03.65, 05.40.J, 47.53, 04.20.G
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تاریخ انتشار 2010