Geometrization of Quantum Mechanics

TL;DR

This paper demonstrates how different formulations of Quantum Mechanics can be represented geometrically, offering a unified perspective that complements traditional algebraic approaches.

Contribution

It introduces a geometric framework for Quantum Mechanics using the momentum map, providing an alternative to the GNS construction for pure states.

Findings

Unified geometric description of quantum states and observables

Alternative to GNS construction for pure states

Framework applicable to various quantum representations

Abstract

We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.