Lie algebra cohomology and group structure of gauge theories

We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincar\'e duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator $Q^{\dagger}$ for the Lie algebra cohomology induced by BRST generator $Q$. We also point out an interesting duality relation - Poincar\'e duality - with respect to gauge anomalies and Wess-Zumino-Witten topological terms. We consider the consistent embedding of the BRST adjoint generator $Q^{\dagger}$ into the relativistic phase space and identify the noncovariant symmetry recently discovered in QED with the BRST adjoint N\"other charge $Q^{\dagger}$.Comment: 24 pages, RevTex, Revised version submitted to J. Math. Phy

Cauchy problem for the Boltzmann-BGK model near a global Maxwellian

In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth solution if the initial perturbation is sufficiently small in a high order energy norm. We also establish an asymptotic decay estimate and uniform $L^2$-stability for nonlinear perturbations.Comment: 26 page

Measurement of statistical evidence on an absolute scale following thermodynamic principles

Statistical analysis is used throughout biomedical research and elsewhere to assess strength of evidence. We have previously argued that typical outcome statistics (including p-values and maximum likelihood ratios) have poor measure-theoretic properties: they can erroneously indicate decreasing evidence as data supporting an hypothesis accumulate; and they are not amenable to calibration, necessary for meaningful comparison of evidence across different study designs, data types, and levels of analysis. We have also previously proposed that thermodynamic theory, which allowed for the first time derivation of an absolute measurement scale for temperature (T), could be used to derive an absolute scale for evidence (E). Here we present a novel thermodynamically-based framework in which measurement of E on an absolute scale, for which "one degree" always means the same thing, becomes possible for the first time. The new framework invites us to think about statistical analyses in terms of the flow of (evidential) information, placing this work in the context of a growing literature on connections among physics, information theory, and statistics.Comment: Final version of manuscript as published in Theory in Biosciences (2013

Growth control of oxygen stoichiometry in homoepitaxial SrTiO3 films by pulsed laser epitaxy in high vacuum

In many transition metal oxides (TMOs), oxygen stoichiometry is one of the most critical parameters that plays a key role in determining the structural, physical, optical, and electrochemical properties of the material. However, controlling the growth to obtain high quality single crystal films having the right oxygen stoichiometry, especially in a high vacuum environment, has been viewed as a challenge. In this work, we show that through proper control of the plume kinetic energy, stoichiometric crystalline films can be synthesized without generating oxygen defects, even in high vacuum. We use a model homoepitaxial system of SrTiO3 (STO) thin films on single crystal STO substrates. Physical property measurements indicate that oxygen vacancy generation in high vacuum is strongly influenced by the energetics of the laser plume, and it can be controlled by proper laser beam delivery. Therefore, our finding not only provides essential insight into oxygen stoichiometry control in high vacuum for understanding the fundamental properties of STO-based thin films and heterostructures, but expands the utility of pulsed laser epitaxy of other materials as well

Emergent Geometry and Quantum Gravity

We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime which causes a noncommutative spacetime at the Planck scale L_P. The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, \omega) and Riemannian geometry (M, g) where the deformations of symplectic structure \omega in terms of electromagnetic fields F=dA are transformed into those of Riemannian metric g. This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity which is thus dubbed as the quantum equivalence principle.Comment: Invited Review for Mod. Phys. Lett. A, 17 page

Optical spectroscopic investigation on the coupling of electronic and magnetic structure in multiferroic hexagonal RMnO3 (R = Gd, Tb, Dy, and Ho) thin films

We investigated the effects of temperature and magnetic field on the electronic structure of hexagonal RMnO3 (R = Gd, Tb, Dy, and Ho) thin films using optical spectroscopy. As the magnetic ordering of the system was disturbed, a systematic change in the electronic structure was commonly identified in this series. The optical absorption peak near 1.7 eV showed an unexpectedly large shift of more than 150 meV from 300 K to 15 K, accompanied by an anomaly of the shift at the Neel temperature. The magnetic field dependent measurement clearly revealed a sizable shift of the corresponding peak when a high magnetic field was applied. Our findings indicated strong coupling between the magnetic ordering and the electronic structure in the multiferroic hexagonal RMnO3 compounds.Comment: 16 pages including 4 figure

Uniform bounds for higher-order semilinear problems in conformal dimension

We establish uniform a-priori estimates for solutions of the semilinear Dirichlet problem \begin{equation} \begin{cases} (-\Delta)^m u=h(x,u)\quad&\mbox{in }\Omega,\\ u=\partial_nu=\cdots=\partial_n^{m-1}u=0\quad&\mbox{on }\partial\Omega, \end{cases} \end{equation} where $h$ is a positive superlinear and subcritical nonlinearity in the sense of the Trudinger-Moser-Adams inequality, either when $\Omega$ is a ball or, provided an energy control on solutions is prescribed, when $\Omega$ is a smooth bounded domain. The analogue problem with Navier boundary conditions is also studied. Finally, as a consequence of our results, existence of a positive solution is shown by degree theory.Comment: Minor correction

Seiberg-Witten-type Maps for Currents and Energy-Momentum Tensors in Noncommutative Gauge Theories

We derive maps relating the currents and energy-momentum tensors in noncommutative (NC) gauge theories with their commutative equivalents. Some uses of these maps are discussed. Especially, in NC electrodynamics, we obtain a generalization of the Lorentz force law. Also, the same map for anomalous currents relates the Adler-Bell-Jackiw type NC covariant anomaly with the standard commutative-theory anomaly. For the particular case of two dimensions, we discuss the implications of these maps for the Sugawara-type energy-momentum tensor.Comment: 14 pages, JHEP styl