Based on the String-mode Loop Regularization method developed recently by Yue-Liang Wu, all one-loop renormalization constants for Non-Abelian gauge theory are computed in details, the resulting renormalization constants are manifestly shown to satisfy Ward-Takahaski-Slavnov-Taylor identities, and lead to the well-known one loop β function for Non-Abelian gauge theory of QCD, which explicitly shown the String-mode Loop Regularization preserves non-abelian gauge symmetry and maintains the divergent behavior of original theory in four dimension.

The radiatively induced Lorentz and CPT violating Chern-Simons terms in QED was also calculated by adopting the String-mode Loop Regularization method, it enables us to make general comments on the various results in literature and obtain a consistent result when simultaneously combining the evaluation for the chiral anomaly which has a unique form once the vector current is kept conserved.

The String-mode Loop Regularization has successfully applied to the underlying gauge theory, effective quantum field theory with dynamically generated spontaneous symmetry breaking, chiral anomaly and gravitational field theory.

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