The Unique Path Lifting for Noncommutative Covering Projections

This article contains a noncommutative generalization of the topological path lifting problem. Noncommutative geometry has no paths and even points. However there are paths of *-automorphisms. It is proven that paths of *-automorphisms comply with unique path lifting.Comment: 11 pages, 12 references. arXiv admin note: substantial text overlap with arXiv:1405.185

Noncommutative Generalization of Wilson Lines

A classical Wilson line is a cooresponedce between closed paths and elemets of a gauge group. However the noncommutative geometry does not have closed paths. But noncommutative geometry have good generalizations of both: the covering projection, and the group of covering transformations. These notions are used for a construction of noncommutative Wilson lines. Wilson lines can also be constructed as global pure gauge fields on the universal covering space. The noncommutative analog of this construction is also developed.Comment: 13 pages, 16 reference