A new gauge-invariant regularization scheme based on Lorentz-invariant noncommutative quantum field theory

IR/UV mixing in non-commutative (NC) field theory is investigated in the Carlson-Carone-Zobin (CCZ) formalism of Lorentz-invariant NC field theory with the assumption that the fields are 'independent' of the 'internal' coordinates theta(munu). A new regularization scheme called 'NC regularization' is then proposed. This scheme removes the Lorentz-invariant IR singularity by subtraction from the theory. It requires the usual UV limit A --> infinity to be accompanied by the commutative limit a --> 0 with Lambda(2)a(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 the phi(3) model. It is shown that the new regularization is gauge-invariant 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, possess a Lorentz-invariant IR singularity which should be 'subtracted off' at zero external momentum squared. This subtraction leads to the same result as the renormalized one obtained by Pauli-Villars-Gupta or dimensional regularizations. Other diagrams with three-point vertices that 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(2)a(2) --> 0. Lorentz-invariant NC phi(4) and scalar Yukawa models are also studied in the one-loop approximation. A comment is made that Lorentz invariance might lead to a decoupling of U(1) from SU(N) in NC U(N) gauge theory.