Tensorial description of quantum mechanics

TL;DR

This paper introduces a tensorial, differential geometric framework for quantum mechanics in the Heisenberg picture, enabling a covariant formulation under all diffeomorphisms.

Contribution

It replaces algebraic structures with tensor fields on the state space, providing a novel geometric perspective on quantum mechanics.

Findings

Enables covariant formulation of quantum mechanics

Replaces algebraic structures with tensor fields

Provides a geometric approach compatible with diffeomorphisms

Abstract

Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a covariant formulation of quantum mechanics under the full diffeomorphism group.