The Weyl bundle as a differentiable manifold

TL;DR

This paper constructs an infinite-dimensional differentiable manifold called ${\mathbb R}^{\infty}$, explores the Weyl algebra bundle's structures, and develops a Fedosov-type star product using connection theory.

Contribution

It introduces a novel infinite-dimensional manifold model and details the differential and metric structures of Weyl algebra bundles, including a new star product construction.

Findings

Construction of ${\mathbb R}^{\infty}$ as a differentiable manifold.

Proof of continuity of the $\

Development of a Fedosov-type star product using connection theory.

Abstract

Construction of an infinite dimensional differentiable manifold ${\mathbb R}^{\infty}$ not modelled on any Banach space is proposed. Definition, metric and differential structures of a Weyl algebra and a Weyl algebra bundle are presented. Continuity of the $\circ$-product in the Tichonov topology is proved. Construction of the $*$-product of the Fedosov type in terms of theory of connection in a fibre bundle is explained.