The Gribov problem in Noncommutative gauge theory

After reviewing Gribov ambiguity of non-Abelian gauge theories, a phenomenon related to the topology of the bundle of gauge connections, we show that there is a similar feature for noncommutative QED over Moyal space, despite the structure group being Abelian, and we exhibit an infinite number of solutions for the equation of Gribov copies. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.Comment: 14 pages. Prepared for the XXV International Fall Workshop on Geometry and Physics, Instituto de Estructura de la Materia (CSIC) Madrid, Spain August 29 - September 02, 201

SL(2,R) Yang-Mills theory on a circle

The kinematics of SL(2,R) Yang-Mills theory on a circle is considered, for reasons that are spelled out. The gauge transformations exhibit hyperbolic fixed points, and this results in a physical configuration space with a non-Hausdorff "network" topology. The ambiguity encountered in canonical quantization is then much more pronounced than in the compact case, and can not be resolved through the kind of appeal made to group theory in that case.Comment: 10 pages, Goteborg ITP 94-19, Contains two files: A latex file with all figures drawn in latex and a tar archive including a slightly modified latex file (uses psfig) and nicer postscript figures+necessary macro

A sketching interface for 3D modeling of polyhedron

We present an intuitive and interactive freehand sketching interface for 3D polyhedrons reconstruction. The interface mimics sketching with pencil on paper and takes freehand sketches as input directly. The sketching environment is natural by allowing sketching with discontinuous, overlapping and multiple strokes. The input sketch is a natural line drawing with hidden lines removed that depicts a 3D object in an isometric view. The line drawing is interpreted by a series of 2D tidy-up processes to produce a vertex-edge graph for 3D reconstruction. A novel reconstruction approach based on three-line-junction analysis and planarity constraint is then used to approximate the 3D geometry and topology of the graph. The reconstructed object can be transformed so that it can be viewed from different viewpoints for interactive design or as immediate feedback to the designers. A new sketch can then be added to the existing 3D object, and reconstructed into 3D by referring to the existing 3D object from the current viewpoint. The incremental modeling enables a 3D object to be reconstructed from multiple sketching sessions from different viewpoints. However, the interface is limited to reconstructing trihedrons from sketches without T-junctions to avoid ambiguity in the hidden topology determination

Constrained S^min\sqrt{\hat{S}_{min}} and reconstructing with semi-invisible production at hadron colliders

Mass variable \sqrt{\hat{S}_{min}} and its variants were constructed by minimising the parton level center of mass energy that is consistent with all inclusive measurements. They were proposed to have the ability to measure mass scale of new physics in a fully model independent way. In this work we relax the criteria by assuming the availability of partial informations of new physics events and thus constraining this mass variable even further. Starting with two different classes of production topology, i.e. antler and non-antler, we demonstrate the usefulness of these variables to constrain the unknown masses. This discussion is illustrated with different examples, from the standard model Higgs production and beyond standard model resonance productions leading to semi-invisible production. We also utilise these constrains to reconstruct the semi-invisible events with the momenta of invisible particles and thus improving the measurements to reveal the properties of new physics.Comment: v2: typos corrected, references added; Matches with published version. 22 pages, 14 figure

Uniqueness of the Fock quantization of scalar fields in spatially flat cosmological spacetimes

We study the Fock quantization of scalar fields in (generically) time dependent scenarios, focusing on the case in which the field propagation occurs in --either a background or effective-- spacetime with spatial sections of flat compact topology. The discussion finds important applications in cosmology, like e.g. in the description of test Klein-Gordon fields and scalar perturbations in Friedmann-Robertson-Walker spacetime in the observationally favored flat case. Two types of ambiguities in the quantization are analyzed. First, the infinite ambiguity existing in the choice of a Fock representation for the canonical commutation relations, understandable as the freedom in the choice of inequivalent vacua for a given field. Besides, in cosmological situations, it is customary to scale the fields by time dependent functions, which absorb part of the evolution arising from the spacetime, which is treated classically. This leads to an additional ambiguity, this time in the choice of a canonical pair of field variables. We show that both types of ambiguities are removed by the requirements of (a) invariance of the vacuum under the symmetries of the three-torus, and (b) unitary implementation of the dynamics in the quantum theory. In this way, one arrives at a unique class of unitarily equivalent Fock quantizations for the system. This result provides considerable robustness to the quantum predictions and renders meaningful the confrontation with observation.Comment: 15 pages, version accepted for publication in JCA