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

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. © 2010 Springer Science+Business Media, LLC.

Año de publicación:

2010

Keywords:

• Vacuum energy
• Nonlinear Quantum Mechanics
• Noncommutative phase spaces
• Scale fractal calculus

Fuente:

scopus