Effective Framework of κ-Minkowski Spacetime and Its Application

An effective Minkowski spacetime having no deformation in formal is established by introducing a well-defined proper time from the κ-deformed Minkowski spacetime related to the standard basis. The κ-Minkowski spacetime connects with a special curved spacetime through this effective spacetime. In the framework of such an effective Minkowski spacetime as a mapped coordinate system of the κ-deformed Minkowski spacetime, models of field theory can be constructed by simply considering the requirement of the Lorentz invariance, and their κ-deformed, i.e. noncommutative effects are comprised naturally. In particular, a kind of fuzziness in the temporal dimension related to noncommutativity is found in the effective framework of the κ-Minkowski spacetime. As an application, three types of formulations of chiral bosons are investigated and consistent results are obtained. PACS Number(s): 02.40.Gh; 11.10.Nx; 11.10.Kk