A Unified Gravity-Electroweak Model Based on a Generalized Yang-Mills Framework

Gravitational and electroweak interactions can be unified in analogy with the unification in the Weinberg-Salam theory. The Yang-Mills framework is generalized to include space-time translational group T(4), whose generators T_{\mu}(=\p/\p x^{\mu}) do not have constant matrix representations. By gauging $T(4) \times SU(2) \times U(1)$ in flat space-time, we have a new tensor field $\phi_{\mu\nu}$ which universally couples to all particles and anti-particles with the same constant $g$, which has the dimension of length. In this unified model, the T(4) gauge symmetry dictates that all wave equations of fermions, massive bosons and the photon in flat space-time reduce to a Hamilton-Jacobi equation with the same `effective Riemann metric tensor' in the geometric-optics limit. Consequently, the results are consistent with experiments. We demonstrated that the T(4) gravitational gauge field can be quantized in inertial frames.Comment: 12 pages. To be published in "Modern Physics Letters A

Space-time translational gauge identities in Abelian Yang-Mills gravity

We derive and calculate the space-time translational gauge identities in quantum Yang-Mills gravity with a general class of gauge conditions involving two arbitrary parameters. These identities of the Abelian group of translation are a generalization of Ward-Takahasi-Fradkin identities and important for general discussions of possible renormalization of Yang-Mills gravity with translational gauge symmetry. The gauge identities in Yang-Mills gravity with a general class of gauge conditions are substantiated by explicit calculations.Comment: 15 pages. To be published in The European Physical Journal - Plus (2012

Quantum Yang-Mills gravity in flat space-time and effective curved space-time for motions of classical objects

Yang-Mills gravity with translational gauge group T(4) in flat space-time implies a simple self-coupling of gravitons and a truly conserved energy-momentum tensor. Its consistency with experiments crucially depends on an interesting property that an `effective Riemannian metric tensor' emerges in and only in the geometric-optics limit of the photon and particle wave equations. We obtain Feynman rules for a coupled graviton-fermion system, including a general graviton propagator with two gauge parameters and the interaction of ghost particles. The equation of motion of macroscopic objects, as an N-body system, is demonstrated as the geometric-optics limit of the fermion wave equation. We discuss a relativistic Hamilton-Jacobi equation with an `effective Riemann metric tensor' for the classical particles.Comment: 20 pages, to be published in "The European Physical Journal - Plus"(2011). The final publication is available at http://www.epj.or

Weighted sampling of outer products

This note gives a simple analysis of the randomized approximation scheme for matrix multiplication of Drineas et al (2006) with a particular sampling distribution over outer products. The result follows from a matrix version of Bernstein's inequality. To approximate the matrix product $AB^\top$ to spectral norm error $\varepsilon\|A\|\|B\|$, it suffices to sample on the order of $(\mathrm{sr}(A) \vee \mathrm{sr}(B)) \log(\mathrm{sr}(A) \wedge \mathrm{sr}(B)) / \varepsilon^2$ outer products, where $\mathrm{sr}(M)$ is the stable rank of a matrix $M$

Time Domain Steady-State Torque Calculation of Voltage Source Pulse-Width-Modulated Inverter Fed Induction Motors, Part I: Theoretical Analysis

Evaluation of torque pulsation associated with the harmonics of pulse width modulated (PWM) inverter-fed drives is important for a quiet and smooth operation. This paper discusses an analytical method for the steady state torque calculation of the voltage source PWM inverter fed induction motors. Equations derived from the 1-2-0 coordinate system are used. A sample calculation is included for the illustration of practical application.Center for Electromechanic