  A quantum theory of noncommutative fields was recently proposed by Carmona,
Cortez, Gamboa and Mendez (hep-th/0301248). The implications of the
noncommutativity 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 an
analogy with previous results on the so-called ``noncommutative harmonic
oscillator construction". Some departures from Lorentz symmetry turned out to
play a key role in the emerging framework. We first consider the same
hamiltonian proposed in hep-th/0301248, and we show that the theory can be
analyzed straightforwardly within the framework of Heisenberg evolution
equation without any need of making reference to the ``noncommutative harmonic
oscillator construction". We then consider a rather general class of
alternative hamiltonians, and we observe that violations of Lorentz invariance
are inevitably encountered. These violations must therefore be viewed as
intrinsically associated with the proposed type of noncommutativity of fields,
rather than as a consequence of a specific choice of Hamiltonian.
