The geometry of real reducible polarizations in quantum mechanics. (8th February 2017)

• Record Type: Journal Article
• Authors: Prieto, Carlos Tejero; Vitolo, Raffaele
• Is Part Of: Journal of physics. Volume 50:Number 10(2017)
• Publication Date: 2017-02-08
• Subjects: geometric quantization -- real polarization -- Schroedinger equation in curved spaces; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa58c7
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: The formulation of geometric quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the polarization bundle. The existence of reducible quantum structures leads to considering the class of Liouville symplectic manifolds. Our main application of this modified geometric quantization scheme is to quantum mechanics on Riemannian manifolds. With this method we obtain an energy operator without the scalar curvature term that appears in the standard formulation, thus agreeing with the usual expression found in the physics literature.