Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The application of star-products to noncommutative geometry and gauge
  theory   We develop a formalism to realize algebras defined by relations on function
spaces. For this porpose we construct the Weyl-ordered star-product and present
a method how to calculate star-products with the help of commuting vector
fields. Concepts developed in noncommutative differential geometry will be
applied to this type of algebras and we construct actions for noncommutative
field theories. Derivations of star-products makes it further possible to
extend noncommutative gauge theory in the Seiberg-Witten formalism with
covariant derivatives. In the commutative limit these theories are becoming
gauge theories on curved backgrounds. We study observables of noncommutative
gauge theories and extend the concept of so called open Wilson lines to general
noncommutative gauge theories.

35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics