Canonical approach to noncommutative gauge theory

It is known that gauge transformation of the Kalb-Ramond field Bμν with vector parameter Λμ is symmetry of the closed string world-sheet action. It fails at the end points of the open string and can be restored by introducing Maxwell field Aμ. We show that the same conclusion valid for space-time equations of motion, because they are conditions for conformal invariance of the world-sheet action. This is example how the symmetries of space-time theory can be investigated using properties of σ-model energy-momentum tensor. We also show that the reducible part of the closed string symmetry transformation, with Λμ=∂μλ, turns to irreducible part of the open string one. As well as Maxwell field Aμ, the parameter λ is nontrivial only on the string endpoints. We show that after quantization the symmetry transformations of the background fields Bμν and Aμ turn to the modified symmetries defined in terms of Moyal star product. The modified Λμ-transformation related different regularizations as well as Seiberg-Witten map.