UV finite field theories on noncommutative spacetimes: The quantum Wick product and time independent perturbation theory

An energy correction is calculated in the time-independent perturbation setup using a regularized ultraviolet finite Hamiltonian on the noncommutative Minkowski space. The correction to the energy is invariant under rotation and translation but is not Lorentz covariant, and this leads to a distortion of the dispersion relation. In the limit where the noncommutativity vanishes, the common quantum field theory on the commutative Minkowski space is reobtained. The calculations are restricted to the regularized cubic interaction.