Application of geometric quantization in quantum mechanics

Jędrzej Śniatycki

Jędrzej Śniatycki

Gennadi Aleksandrovich Sardanashvily

Carlos Prieto, Raffaele F. Vitolo

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.

Jincheng Zhang

This paper explores the application of probabilistic geometry to the theoretical framework of quantum computation, specifically focusing on the development of a quantum geometric quantization model. We propose a novel approach that integrates geometric structures and probabilistic logic to provide a deeper understanding of quantum systems and to guide the optimization of quantum algorithms. The core mechanism centers around representing quantum states as probability distributions, allowing for a more nuanced and robust analysis of quantum phenomena. This framework offers a new perspective on the design and analysis of quantum algorithms, potentially unlocking significant advancements in computational complexity.

Enrico Santamato