Correlation Functions in Two-Dimensional Dilaton Gravity

The Liouville approach is applied to the quantum treatment of the dilaton gravity in two dimensions. The physical states are obtained from the BRST cohomology and correlation functions are computed up to three-point functions. For the $N=0$ case (i.e., without matter), the cosmological term operator is found to have the discrete momentum that plays a special role in the $c=1$ Liouville gravity. The correlation functions for arbitrary numbers of operators are found in the $N=0$ case, and are nonvanishing only for specific ``chirality'' configurations.Comment: 14 pages, TIT/HEP-204, STUPP-92-13

Derived bracket construction and Manin products

We will extend the classical derived bracket construction to any algebra over a binary quadratic operad. We will show that the derived product construction is a functor given by the Manin white product with the operad of permutation algebras. As an application, we will show that the operad of prePoisson algebras is isomorphic to Manin black product of the Poisson operad with the preLie operad. We will show that differential operators and Rota-Baxter operators are, in a sense, Koszul dual to each other.Comment: This is the final versio

On why the Iron K-shell absorption in AGN is not a signature of the local Warm/Hot Intergalactic Medium

We present a comparison between the 2001 XMM-Newton and 2005 Suzaku observations of the quasar, PG1211+143 at z=0.0809. Variability is observed in the 7 keV iron K-shell absorption line (at 7.6 keV in the quasar frame), which is significantly weaker in 2005 than during the 2001 XMM-Newton observation. From a recombination timescale of <4 years, this implies an absorber density n>0.004 particles/cm3, while the absorber column is 5e22<N_H <1 1e24 particles/cm2. Thus the sizescale of the absorber is too compact (pc scale) and the surface brightness of the dense gas too high (by 9-10 orders of magnitude) to arise from local hot gas, such as the local bubble, group or Warm/Hot Intergalactic Medium (WHIM), as suggested by McKernan et al. (2004, 2005). Instead the iron K-shell absorption must be associated with an AGN outflow with mildly relativistic velocities. Finally we show that the the association of the absorption in PG1211+143 with local hot gas is simply a coincidence, the comparison between the recession and iron K absorber outflow velocities in other AGN does not reveal a one to one kinematic correlation.Comment: accepted for publication in MNRAS LETTERS. 5 pages, 4 figure

Extended supersymmetry and its reduction on a circle with point singularities

We investigate $N$-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer $n$, $N=2n+1$ supercharges are explicitly constructed in terms of discrete transformations, and a class of singularities compatible with supersymmetry is clarified. In our formulation, the supersymmetry can be reduced to $M$-extended supersymmetry for any integer $M<N$. The degeneracy of the spectrum and spontaneous supersymmetry breaking are also studied.Comment: 36 pages, 5 figures, 2 table

Leibniz 2-algebras and twisted Courant algebroids

In this paper, we give the categorification of Leibniz algebras, which is equivalent to 2-term sh Leibniz algebras. They reveal the algebraic structure of omni-Lie 2-algebras introduced in \cite{omniLie2} as well as twisted Courant algebroids by closed 4-forms introduced in \cite{4form}. We also prove that Dirac structures of twisted Courant algebroids give rise to 2-term $L_\infty$-algebras and geometric structures behind them are exactly $H$-twisted Lie algebroids introduced in \cite{Grutzmann}.Comment: 22 pages, to appear in Comm. Algebr

Spectral properties on a circle with a singularity

We investigate the spectral and symmetry properties of a quantum particle moving on a circle with a pointlike singularity (or point interaction). We find that, within the U(2) family of the quantum mechanically allowed distinct singularities, a U(1) equivalence (of duality-type) exists, and accordingly the space of distinct spectra is U(1) x [SU(2)/U(1)], topologically a filled torus. We explore the relationship of special subfamilies of the U(2) family to corresponding symmetries, and identify the singularities that admit an N = 2 supersymmetry. Subfamilies that are distinguished in the spectral properties or the WKB exactness are also pointed out. The spectral and symmetry properties are also studied in the context of the circle with two singularities, which provides a useful scheme to discuss the symmetry properties on a general basis.Comment: TeX, 26 pages. v2: one reference added and two update

Quantum Analogy of Poisson Geometry, Related Dendriform Algebras and Rota-Baxter Operators

We will introduce an associative (or quantum) version of Poisson structure tensors. This object is defined as an operator satisfying a "generalized" Rota-Baxter identity of weight zero. Such operators are called generalized Rota-Baxter operators. We will show that generalized Rota-Baxter operators are characterized by a cocycle condition so that Poisson structures are so. By analogy with twisted Poisson structures, we propose a new operator "twisted Rota-Baxter operators" which is a natural generalization of generalized Rota-Baxter operators. It is known that classical Rota-Baxter operators are closely related with dendriform algebras. We will show that twisted Rota-Baxter operators induce NS-algebras which is a twisted version of dendriform algebra. The twisted Poisson condition is considered as a Maurer-Cartan equation up to homotopy. We will show the twisted Rota-Baxter condition also is so. And we will study a Poisson-geometric reason, how the twisted Rota-Baxter condition arises.Comment: 18 pages. Final versio

Distillation of Liquid Xenon to Remove Krypton

A high performance distillation system to remove krypton from xenon was constructed, and a purity level of Kr/Xe = $\sim 3 \times 10^{-12}$ was achieved. This development is crucial in facilitating high sensitivity low background experiments such as the search for dark matter in the universe.Comment: 15 pages, 11 figure