Geometrical description of algebraic structures: Applications to Quantum Mechanics

TL;DR

This paper explores how geometrical methods can be systematically applied to quantum mechanics by transitioning from algebraic to geometric structures, emphasizing the Jordan-Lie framework to deepen understanding of quantum theories.

Contribution

It introduces a systematic approach to geometrize quantum theories, focusing on the Jordan-Lie structure, bridging algebraic and geometric perspectives in quantum mechanics.

Findings

Systematic transition from algebraic to geometric structures in quantum theories.

Application of Jordan-Lie structure to analyze quantum geometries.

Enhanced understanding of quantum mechanics through geometrization methods.

Abstract

Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to quantum mechanics. We will concentrate our attention into quantum theories and we will show how to use in a systematic way the transition from algebraic to geometrical structures to explore their geometry, mainly its Jordan-Lie structure.