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Through defining irreducible loop integrals (ILIs), a set of consistencyconditions for the regularized (quadratically and logarithmically) divergentILIs are obtained to maintain the generalized Ward identities of gaugeinvariance in non-Abelian gauge theories. Overlapping UV divergences areexplicitly shown to be factorizable in the ILIs and be harmless via suitablesubtractions. A new regularization and renormalization method is presented inthe initial space-time dimension of the theory. The procedure respectsunitarity and causality. Of interest, the method leads to an infinity freerenormalization and meanwhile maintains the symmetry principles of the originaltheory except the intrinsic mass scale caused conformal scaling symmetrybreaking and the anomaly induced symmetry breaking. Quantum field theories(QFTs) regularized through the new method are well defined and governed by aphysically meaningful characteristic energy scale (CES) $M_c$ and a physicallyinteresting sliding energy scale (SES) $\mu_s$ which can run from $\mu_s \simM_c$ to a dynamically generated mass gap $\mu_s=\mu_c$ or to $\mu_s =0$ in theabsence of mass gap and infrared (IR) problem. It is strongly indicated thatthe conformal scaling symmetry and its breaking mechanism play an importantrole for understanding the mass gap and quark confinement.Comment: 59 pages, Revtex, 4 figures, 1 table, Erratum added, published  versio

SYMMETRY PRINCIPLE PRESERVING AND INFINITY FREE REGULARIZATION AND RENORMALIZATION OF QUANTUM FIELD THEORIES AND THE MASS GAP