The group of Hamiltonian automorphisms of a star product

TL;DR

This paper explores the deformation of Hamiltonian diffeomorphisms into Hamiltonian automorphisms within deformation quantization, analyzing the resulting group's geometry and the Flux morphism's deformation.

Contribution

It introduces a deformation of the Hamiltonian diffeomorphism group into Hamiltonian automorphisms of a star product and studies its geometric properties and Flux morphism deformation.

Findings

Deformation of the Hamiltonian diffeomorphism group into automorphisms.

Analysis of the group's geometric structure.

Deformation of the Flux morphism in the quantization framework.

Abstract

We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.