On Nonlinear Quantum Mechanics,Noncommutative Phase Spaces,Fractal-Scale Calculus and Vacuum Energy |
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Authors: | Carlos Castro |
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Institution: | 1.Center for Theoretical Studies of Physical Systems,Clark Atlanta University,Atlanta,USA |
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Abstract: | A (to our knowledge) novel 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. |
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