  The IR/UV mixing in the non-commutative (NC) field theory is investigated in
Carlson-Carone-Zobin (CCZ) formalism of Lorentz-invariant NC field theory
provided that the fields are `independent' of the `internal' coordinates
$\theta^{\mu\nu}$. A new regularization scheme called NC regularizatioon is
then proposed, which removes the Lorentz-invariant IR singularity from the
theory. It requires the usual UV limit $\Lambda\to \infty$ to be accompanied
with the commutative limit $a\to 0$ with $\Lambda^2a^2$ fixed, where $a$ is the
length parameter in the theory. The new UV limit gives the usual renormalized
amplitude of the one-loop self-energy diagram of $\phi^3$ model. It is shown
that the new regularization is gauge-invariant, that is, the non-transverse
part of the vacuum polarization in QED is automatically transverse in
Lorentz-invariant NCQED but the two transverse pieces, one of which is already
transverse in QED, possesses Lorentz-invariant IR singularity which should be
`subtracted off' at zero external momentum squared. The subtraction leads to
the same result as the renormalized one by Pauli-Villars or dimensional
regularizations. Other diagrams with three-point vertices which contribute to
the photon self-energy in Lorentz-non-invariant NCQED all vanish due to Lorentz
invariance under the assumption adopted, while the tadpole diagram gives a
finite contribution to the charge renormalization which vanishes if $
Lambda^2a^2\to 0$. Lorentz-invariant NC $\phi^4$ and scalar Yukawa models are
also discussed in the one-loop approximation. A comment is made that
Lorentz-invariance might lead to a decoupling of U(1) part from SU(N) in NC
U(N) gauge theory.
