  We propose a noncommutative extension of the Minkowski spacetime by
introducing a well-defined proper time from the kappa-deformed Minkowski
spacetime related to the standard basis. The extended Minkowski spacetime is
commutative, i.e. it is based on the standard Heisenberg commutation relations,
but some information of noncommutativity is encoded through the proper time to
it. Within this framework, by simply considering the Lorentz invariance we can
construct field theory models that comprise noncommutative effects naturally.
In particular, we find a kind of temporal fuzziness related to noncommutativity
in the noncommutative extension of the Minkowski spacetime. As a primary
application, we investigate three types of formulations of chiral bosons,
deduce the lagrangian theories of noncommutative chiral bosons and quantize
them consistently in accordance with Dirac's method, and further analyze the
self-duality of the lagrangian theories in terms of the parent action approach.
