Symmetry Principle Preserving and Infinity Free Regularization and Renormalization of Quantum Field Theories and the Mass Gap
Abstract
Through defining irreducible loop integrals (ILI's), a set of consistency conditions for the regularized (quadratically and logarithmically) divergent ILI's are obtained to maintain the generalized Ward identities of gauge invariance in nonAbelian gauge theories. The ILI's of arbitrary loop graphs can be evaluated from the corresponding Feynman loop integrals by adopting an ultraviolet (UV) divergence preserving parameter method. Overlapping UV divergences are explicitly shown to be factorizable in the ILI's and be harmless via suitable subtractions. A new regularization and renormalization method is presented in the initial spacetime dimension of the theory. The procedure respects unitarity and causality. Of interest, the method leads to an infinity free renormalization and meanwhile maintains the symmetry principles of the original theory except the intrinsic mass scale caused conformal scaling symmetry breaking and the anomaly induced symmetry breaking. Tadpole graphs of YangMills gauge fields are found to play an essential role for maintaining manifest gauge invariance via cancellations of quadratically divergent ILI's. Quantum field theories (QFT's) regularized through the new method are well defined and governed by a physically meaningful characteristic energy scale (CES) M_{c} and a physically interesting sliding energy scale (SES) μ_{s} which can run from μ_{s} ~ M_{c} to a dynamically generated mass gap μ_{s} = μ_{c} or to μ_{s} = 0 in the absence of mass gap and infrared (IR) problem. For M_{c} → ∞, the initial UV divergent properties of QFT's are recovered and welldefined. In fact, the CES M_{c} and SES at μ_{s} = μ_{c} play the role of UV and IR cutoff energy scales respectively. It is strongly indicated that the conformal scaling symmetry and its breaking mechanism play an important role for understanding the mass gap and quark confinement. The new method is developed to be applicable for both underlying renormalizable QFT's and effective QFT's. It also leads to a set of conjectures on mathematically interesting numbers and functional limits which may provide deep insights in mathematics.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 2003
 DOI:
 10.1142/S0217751X03015222
 arXiv:
 arXiv:hepth/0209021
 Bibcode:
 2003IJMPA..18.5363W
 Keywords:

 11.10.z;
 11.15.q;
 11.15.Bt;
 Field theory;
 Gauge field theories;
 General properties of perturbation theory;
 High Energy Physics  Theory;
 High Energy Physics  Phenomenology
 EPrint:
 59 pages, Revtex, 4 figures, 1 table, Erratum added, published version