The Weyl bundle as a differentiable manifold

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 $\ast$-product of the Fedosov type in terms of theory of connection in a fibre bundle is explained.

31 pages; revised version - some typoes have been eliminated, notation has been simplified