Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-I

TL;DR

This paper explores the geometric structures underlying quantum mechanics, including symplectic and Fubini-Study geometries, aiming to connect quantum theory with classical gravity through geometric insights.

Contribution

It analyzes the geometry of quantum mechanics in both classical phase space and projective Hilbert space, highlighting potential links to gravity.

Findings

Geometry of quantum states in phase space and projective space elucidated

Potential implications for understanding gravity through quantum geometry

Discussion of symplectic structures and Fubini-Study metric in quantum contexts

Abstract

The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.