Conformal Scaling Gauge Symmetry and Inflationary Universe

Considering the conformal scaling gauge symmetry as a fundamental symmetry of nature in the presence of gravity, a scalar field is required and used to describe the scale behavior of universe. In order for the scalar field to be a physical field, a gauge field is necessary to be introduced. A gauge invariant potential action is constructed by adopting the scalar field and a real Wilson-like line element of the gauge field. Of particular, the conformal scaling gauge symmetry can be broken down explicitly via fixing gauge to match the Einstein-Hilbert action of gravity. As a nontrivial background field solution of pure gauge has a minimal energy in gauge interactions, the evolution of universe is then dominated at earlier time by the potential energy of background field characterized by a scalar field. Since the background field of pure gauge leads to an exponential potential model of a scalar field, the universe is driven by a power-law inflation with the scale factor $a(t) \sim t^p$. The power-law index $p$ is determined by a basic gauge fixing parameter $g_F$ via $p = 16\pi g_F^2[1 + 3/(4\pi g_F^2) ]$. For the gauge fixing scale being the Planck mass, we are led to a predictive model with $g_F=1$ and $p\simeq 62$.Comment: 12 pages, RevTex, no figure

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

To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to avoid infinities. The divergence has got us into trouble since developing quantum electrodynamics in 1930s, its treatment via the renormalization scheme is satisfied not by all physicists, like Dirac and Feynman who have made serious criticisms. The renormalization group analysis reveals that QFTs can in general be defined fundamentally with the meaningful energy scale that has some physical significance, which motivates us to develop a new symmetry-preserving and infinity-free regularization scheme called loop regularization (LORE). A simple regularization prescription in LORE is realized based on a manifest postulation that a loop divergence with a power counting dimension larger than or equal to the space-time dimension must vanish. The LORE method is achieved without modifying original theory and leads the divergent Feynman loop integrals well-defined to maintain the divergence structure and meanwhile preserve basic symmetries of original theory. The crucial point in LORE is the presence of two intrinsic energy scales which play the roles of ultraviolet cut-off $M_c$ and infrared cut-off $\mu_s$ to avoid infinities. The key concept in LORE is the introduction of irreducible loop integrals (ILIs) on which the regularization prescription acts, which leads to a set of gauge invariance consistency conditions between the regularized tensor-type and scalar-type ILIs. The evaluation of ILIs with ultraviolet-divergence-preserving (UVDP) parametrization naturally leads to Bjorken-Drell's analogy between Feynman diagrams and electric circuits. The LORE method has been shown to be applicable to both underlying and effective QFTs.Comment: 53 pages, 14 figures, the article in honor of Freeman Dyson's 90th birthday, minor typos corrected, published versio