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

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

Constrained Deep Transfer Feature Learning and its Applications

Feature learning with deep models has achieved impressive results for both data representation and classification for various vision tasks. Deep feature learning, however, typically requires a large amount of training data, which may not be feasible for some application domains. Transfer learning can be one of the approaches to alleviate this problem by transferring data from data-rich source domain to data-scarce target domain. Existing transfer learning methods typically perform one-shot transfer learning and often ignore the specific properties that the transferred data must satisfy. To address these issues, we introduce a constrained deep transfer feature learning method to perform simultaneous transfer learning and feature learning by performing transfer learning in a progressively improving feature space iteratively in order to better narrow the gap between the target domain and the source domain for effective transfer of the data from the source domain to target domain. Furthermore, we propose to exploit the target domain knowledge and incorporate such prior knowledge as a constraint during transfer learning to ensure that the transferred data satisfies certain properties of the target domain. To demonstrate the effectiveness of the proposed constrained deep transfer feature learning method, we apply it to thermal feature learning for eye detection by transferring from the visible domain. We also applied the proposed method for cross-view facial expression recognition as a second application. The experimental results demonstrate the effectiveness of the proposed method for both applications.Comment: International Conference on Computer Vision and Pattern Recognition, 201

Facial Landmark Detection: a Literature Survey

The locations of the fiducial facial landmark points around facial components and facial contour capture the rigid and non-rigid facial deformations due to head movements and facial expressions. They are hence important for various facial analysis tasks. Many facial landmark detection algorithms have been developed to automatically detect those key points over the years, and in this paper, we perform an extensive review of them. We classify the facial landmark detection algorithms into three major categories: holistic methods, Constrained Local Model (CLM) methods, and the regression-based methods. They differ in the ways to utilize the facial appearance and shape information. The holistic methods explicitly build models to represent the global facial appearance and shape information. The CLMs explicitly leverage the global shape model but build the local appearance models. The regression-based methods implicitly capture facial shape and appearance information. For algorithms within each category, we discuss their underlying theories as well as their differences. We also compare their performances on both controlled and in the wild benchmark datasets, under varying facial expressions, head poses, and occlusion. Based on the evaluations, we point out their respective strengths and weaknesses. There is also a separate section to review the latest deep learning-based algorithms. The survey also includes a listing of the benchmark databases and existing software. Finally, we identify future research directions, including combining methods in different categories to leverage their respective strengths to solve landmark detection "in-the-wild"