Heisenberg Evolution in a Quantum Theory of Noncommutative Fields

A quantum theory of noncommutative fields was recently proposed by Carmona,Cortez, Gamboa and Mendez (hep-th/0301248). The implications of thenoncommutativity of the fields, intended as the requirements$[\phi,\phi^{+}]=\theta\delta^{3}(x-x^{\prime}),[\pi,\pi^{+}]=B\delta^{3}(x-x^{\prime}) $, were analyzed on the basis of ananalogy with previous results on the so-called ``noncommutative harmonicoscillator construction". Some departures from Lorentz symmetry turned out toplay a key role in the emerging framework. We first consider the samehamiltonian proposed in hep-th/0301248, and we show that the theory can beanalyzed straightforwardly within the framework of Heisenberg evolutionequation without any need of making reference to the ``noncommutative harmonicoscillator construction". We then consider a rather general class ofalternative hamiltonians, and we observe that violations of Lorentz invarianceare inevitably encountered. These violations must therefore be viewed asintrinsically associated with the proposed type of noncommutativity of fields,rather than as a consequence of a specific choice of Hamiltonian.Comment: 9 page