Quantum Structure of Field Theory and Standard Model Based on Infinity-free Loop Regularization/Renormalization

摘要

To understand better the quantum structure of field theory and standard modelin particle physics, it is necessary to investigate carefully the divergencestructure in quantum field theories (QFTs) and work out a consistent frameworkto avoid infinities. The divergence has got us into trouble since developingquantum electrodynamics in 1930s, its treatment via the renormalization schemeis satisfied not by all physicists, like Dirac and Feynman who have madeserious criticisms. The renormalization group analysis reveals that QFTs can ingeneral be defined fundamentally with the meaningful energy scale that has somephysical significance, which motivates us to develop a new symmetry-preservingand infinity-free regularization scheme called loop regularization (LORE). Asimple regularization prescription in LORE is realized based on a manifestpostulation that a loop divergence with a power counting dimension larger thanor equal to the space-time dimension must vanish. The LORE method is achievedwithout modifying original theory and leads the divergent Feynman loopintegrals well-defined to maintain the divergence structure and meanwhilepreserve basic symmetries of original theory. The crucial point in LORE is thepresence of two intrinsic energy scales which play the roles of ultravioletcut-off $M_c$ and infrared cut-off $\mu_s$ to avoid infinities. The key conceptin LORE is the introduction of irreducible loop integrals (ILIs) on which theregularization prescription acts, which leads to a set of gauge invarianceconsistency conditions between the regularized tensor-type and scalar-typeILIs. The evaluation of ILIs with ultraviolet-divergence-preserving (UVDP)parametrization naturally leads to Bjorken-Drell's analogy between Feynmandiagrams and electric circuits. The LORE method has been shown to be applicableto both underlying and effective QFTs.