New Gauge-Invariant Regularization Scheme Based on Lorentz-Invariant Noncommutative Quantum Field Theory; hep-th/0312080

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 θµν. 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 Λ → ∞ to be accompanied by the commutative limit a → 0 with Λ2a2 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 φ3 model. It is shown that the new regularization is gauge-invariant; the ‘non-transverse ’ part of the vacuum polarization in QED is automat-ically 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 regulariza-tions. 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 assumptio