Remarks on generalized Fedosov algebras

TL;DR

This paper explores a generalized Fedosov algebra framework, analyzing star products, bimodule structures, and trace functionals, with explicit formulas and applications to noncommutative field theories.

Contribution

It introduces a broad class of Fedosov algebras with explicit formulas and discusses their relevance to Seiberg-Witten maps and noncommutative geometry.

Findings

Explicit expressions for star products up to second order.

Existence of a trace functional for the generalized algebras.

Application to noncommutative field theory scenarios.

Abstract

The variant of Fedosov construction based on fairly general fiberwise product in the Weyl bundle is studied. We analyze generalized star products of functions, of sections of endomorphisms bundle, and those generating deformed bimodule structure as introduced previously by Waldmann. Isomorphisms of generalized Fedosov algebras are considered and their relevance for deriving Seiberg-Witten map is described. The existence of the trace functional is established. For star products and for the trace functional explicit expressions, up to second power of deformation parameter, are given. The example of symmetric part of noncommutativity tensor is discussed as a case with possible field-theoretic application.