124095561
THE QUANTUM R-MATRIX VIA CANONICAL QUANTIZATION IN THE LIOUVILLE THEORY
Starting from the classical Liouville theory, we study its quantum theory through canonical quantization. We find that if the Poisson bracket relations between two vectors are dominated by the classical r-matrix in the classical case, their quantum analogue is replaced by the exchange relations dominated by the quantum R-matrix. The quantum group structure in the quantum Liouville theory is studied and the central charge of the quantum Liouville theory is also obtained.
122884461
On the composition laws of Beltrami-Liouville theories and 2D quantum gravity☆
Abstract We present the composition laws or cocycle conditions of the Liouville theory and Beltrami-Liouville theory as well as the quantum gravity in two dimensions. We show that for the 2D gravity, their special cases give rise to the composition laws of Polyakov's light-cone action and that of the geometric action of the Virasoro group. By means of the composition laws, we give the gravitational Ward identities and a relation between the actions of the Liouville theory and the topological gravity and find that the principal action of the 2D topological gravity is a coboundary which should obey a cocylce condition in the Liouville complex.
121280592
The exchange algebra for Liouville field on Riemann surfaces with h>1 genus
We consider the classical Liouville field theory on the Riemann surface with h>1 genus. In terms of the uniformization theorem of the Riemann surface, we show explicitly the classical exchange algebra (CEA) for the chiral components of the Liouville field. We find that this classical exchange algebra is just the same as that on a Riemann sphere with 2h punctures.
121131777
Physics counterpart of quasiconformal transformation, two-dimensional quantum gravity and their symmetries☆
Abstract By using the Gelfand-Dikii bracket of the second kind, we present infinite dimensional symmetries of quasiconformal diffeomorphisms whose special case gives infinite dimensional symmetries of the Virasoro algebra. The physics counterpart of quasiconformal transformation is 2D induced gravity in the light-cone metric whose SL (2, R ) symmetry is reexplored and its quantization is also performed by using the method of conformal field theory.
10586906
Intrinsic Vertex Regularization and Renormalization in $\phi^4$ Field Theory
Based upon the intrinsic relation between the divergent lower point functions and the convergent higher point ones in the renormalizable quantum field theories, we propose a new method for regularization and renormalization in QFT. As an example, we renormalize the $\phi^{4}$ theory at the one loop order by means of this method.
122786546
Field equations, conservation laws in 2D quantum gravity and the Beltrami-KdV-Liouville system
Abstract We present the equations of motion and the conservation laws under various gauges of 2D induced gravity as a kind of the Beltrami-Liouville theory. We generalize the schwarzian derivative and derive its composition law. We also find the relation between the Beltrami-Liouville theory and the KdV system as well as the reccursion relations due to Gel'fand and Dikii based on the properties of the quasiconformal transformations.
119229485
Classification study of WISE infrared sources: identification of candidate asymptotic giant branch stars
In the Wide-field Infrared Survey Explorer (WISE) all-sky source catalog there are 76 million mid-infrared point sources that were detected in the first three WISE bands and have association with only one 2MASS near-IR source within 3′′. We search for their identifications in the SIMBAD database and find 3.2 million identified sources. Based on these known sources, we establish three criteria for selecting candidate asymptotic giant branch (AGB) stars in the Galaxy, which are three defined zones in a color-color diagram, Galactic latitude |b| ≤ 20°, and “corrected” WISE third-band W3 c ≤11. Applying these criteria to the WISE+2MASS sources, 1.37 million of them are selected. We analyze the WISE third-band W3 distribution of the selected sources, and further establish that W3≤8 is required in order to exclude a large fraction of normal stars from them. We therefore find 0.47 million candidate AGB stars in our Galaxy from the WISE source catalog. Using W3 c , we estimate their distances and derive their Galactic distributions. The candidates are generally distributed around the Galactic center uniformly, with 68% (1-σ) of them within approximately 8 kpc. We discuss the idea that optical spectroscopy can be used to verify the C-rich AGB stars in our candidates, and thus a fraction of them (~10%) will be good targets for the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) survey that is planned to start in fall of 2012.
120385604
Von Hove model of quantum field theory‐from the point of view of infinite dimensional stationary Markov process theory
There are two ways to quantize the classical von Hove model. One way is to quantize the classical von Hove field equation, and the other is to quantize the classical energy functional. In this paper, their relation to each other is pointed out. As an application the second‐order approximate quantization of (φ4)2‐kink field is studied.
17172847
Topological graph polynomials and quantum field theory Part I: heat kernel theories
We investigate the relationship between the universal topological polynomials for graphs in mathematics and the parametric representation of Feynman amplitudes in quantum field theory. In this first paper we consider translation invariant theories with the usual heat-kernel-based propagator. We show how the Symanzik polynomials of quantum field theory are particular multivariate versions of the Tutte polynomial, and how the new polynomials of noncommutative quantum field theory are particular versions of the Bollob\'as-Riordan polynomials.
34602223
Probing non-abelian statistics of Majorana fermions in ultracold atomic superfluid.
We propose an experiment to directly probe the non-abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.
119627570
How to Resum Feynman Graphs
In this paper, we reformulate the combinatorial core of constructive quantum field theory. We define universal rational combinatorial weights for pairs made of a graph and any of its spanning trees. These weights are simply the percentage of Hepp’s sectors of the graph in which the tree is leading, in the sense of Kruskal’s greedy algorithm. Our main new mathematical result is an integral representation of these weights in terms of the positive matrix appearing in the symmetric “BKAR” Taylor forest formula. Then, we explain how the new constructive technique called Loop Vertex Expansion reshuffles according to these weights the divergent series of the intermediate field representation into a convergent series which is the Borel sum of the ordinary perturbative Feynman’s series.