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This paper is a review by the authors concerning the construction of a Poincaré covariant (owing to space-time continuum) field-theoretic formalism in terms of step-function-type basis functions without ultraviolet divergences. This formalism analytically derives confinement/deconfinement, mass-gap and Regge trajectory for non-Abelian gauge fields, and gives solutions for self-interacting scalar fields. Fields propagate in space-time continuum and fields with finite degrees of freedom toward continuum limit have no ultraviolet divergence. Basis functions defined in a parameter space-time are mapped to real space-time. The authors derive a new solution comprised of classical fields as vacuum and quantum fluctuations, leading to the linear potential between the particle and antiparticle from the Wilson loop. The Polyakov line gives finite binding energies and reveals the deconfining property at high temperatures. The quantum action yields positive mass from the classical fields and quantum fluctuations produce the Coulomb potential. Pure Yang-Mills fields show the same mass-gap owing to the particle-antiparticle pair creation. The Dirac equation under linear potential is analytically solved in this formalism, reproducing the principal properties of Regge trajectories at a quantum level. Further outlook mentions a possibility of the difference between conventional continuum and present wave functions responsible for the cosmological constant. [ABSTRACT FROM AUTHOR]

The potential (reaction) energy and reaction rate of an accidental sodium−water reaction are investigated for fast breeder nuclear reactor safety. The potential energy is calculated using the molecular orbital method with accurate Gaussian Quadratures in the density functional scheme. The gaseous reaction rate analysis focuses on collision theory rather than transition state theory; the latter of which is more for solvents/solutions. The rate constant was derived using classical molecular dynamics (MDs) in two dimensions (2D) with the rigid sphere model. The MD calculation reveals analytic sequences suppressing error accumulations and time consumptions. The 2D result is converted to the 3D value via a corresponding cross section ratio with a form factor, reproducing the experimental value. The availability of microscopic results to macroscopic flow dynamics is appended; renormalizing the kinematic viscosity coefficient with scale-independent constants. An effective (pseudo-) MD for the heat transfer is also appended. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The antiferromagnetism in an infinite-layer copper oxide CaCuO2 was analyzed by adding a well potential solely to the atomic potential of an O2− ion in constructing a basis set for a Bloch-type periodic linear combination of numerically calculated atomic orbitals. (The well is not added to the solid Hamiltonian.) In this method that solves a secular equation to find all electron states, the original Kohn−Sham local density approximation (LDA) was employed. (Magnetic properties calculated with generalized gradient approximation are more similar to those with the original Kohn−Sham LDA than Vosko−Wilk−Nusair results.) The Cu oxides contain the O2− ion, which is stable in a solid but emits an electron in a vacuum. This implies that the atomic wave equation of electrons for an isolated O2− in a vacuum lacks real solutions unless a well potential is added to the atomic potential. The well potential for the O2− basis set was calculated using the Coulomb potential generated by nuclei and electron clouds surrounding O2− in a solid. A relatively shallow well potential within an ion radius compared to the well depth usually used results in significant delocalization of electrons at the O2− site. This periodic molecular orbital method predicts insulating antiferromagnetic ordering in CaCuO2. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2012 [ABSTRACT FROM AUTHOR]

This article reports studies by Fukushima and coworkers since 1980 concerning their highly accurate numerical integral method using Gaussian quadratures to evaluate the total energy in electronic state calculations. Gauss-Legendre and Gauss-Laguerre quadratures were used for integrals in the finite and infinite regions, respectively. Our previous article showed that, for diatomic molecules such as CO and FeO, elliptic coordinates efficiently achieved high numerical integral accuracy even with a numerical basis set including transition metal atomic orbitals. This article will generalize straightforward details for multiatomic systems with direct integrals in each decomposed elliptic coordinate determined from the nuclear positions of picked-up atom pairs. Sample calculations were performed for the molecules O3 and H2O. This article will also try to present, in another coordinate, a numerical integral by partially using the Becke's decomposition published in 1988, but without the Becke's fuzzy cell generated by the polynomials of internuclear distance between the pair atoms. Instead, simple nuclear weights comprising exponential functions around nuclei are used. The one-center integral is performed with a Gaussian quadrature pack in a spherical coordinate, included in the author's original program in around 1980. As for this decomposition into one-center integrals, sample calculations are carried out for Li2. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [ABSTRACT FROM AUTHOR]

Ultraviolet self-interaction energies in field theory sometimes contain meaningful physical quantities. The self-energies in such as classical electrodynamics are usually subtracted from the rest mass. For the consistent treatment of energies as sources of curvature in the Einstein field equations, this study includes these subtracted self-energies into vacuum energy expressed by the constant Lambda (used in such as Lambda-CDM). In this study, the self-energies in electrodynamics and macroscopic classical Einstein field equations are examined, using the formalisms with the ultraviolet cut-off scheme. One of the cut-off formalisms is the field theory in terms of the step-function-type basis functions, developed by the present authors. The other is a continuum theory of a fundamental particle with the same cut-off length. Based on the effectiveness of the continuum theory with the cut-off length shown in the examination, the dominant self-energy is the quadratic term of the Higgs field at a quantum level (classical self-energies are reduced to logarithmic forms by quantum corrections). The cut-off length is then determined to reproduce today’s tiny value of Lambda for vacuum energy. Additionally, a field with nonperiodic vanishing boundary conditions is treated, showing that the field has no zero-point energy. [ABSTRACT FROM AUTHOR]