Higher gauge theory -- differential versus integral formulation

The term higher gauge theory refers to the generalization of gauge theory to a theory of connections at two levels, essentially given by 1- and 2-forms. So far, there have been two approaches to this subject. The differential picture uses non-Abelian 1- and 2-forms in order to generalize the connection 1-form of a conventional gauge theory to the next level. The integral picture makes use of curves and surfaces labeled with elements of non-Abelian groups and generalizes the formulation of gauge theory in terms of parallel transports. We recall how to circumvent the classic no-go theorems in order to define non-Abelian surface ordered products in the integral picture. We then derive the differential picture from the integral formulation under the assumption that the curve and surface labels depend smoothly on the position of the curves and surfaces. We show that some aspects of the no-go theorems are still present in the differential (but not in the integral) picture. This implies a substantial structural difference between non-perturbative and perturbative approaches to higher gauge theory. We finally demonstrate that higher gauge theory provides a geometrical explanation for the extended topological symmetry of BF-theory in both pictures.Comment: 26 pages, LaTeX with XYPic diagrams; v2: typos corrected and presentation improve

Holonomic quantum computation in the presence of decoherence

We present a scheme to study non-abelian adiabatic holonomies for open Markovian systems. As an application of our framework, we analyze the robustness of holonomic quantum computation against decoherence. We pinpoint the sources of error that must be corrected to achieve a geometric implementation of quantum computation completely resilient to Markovian decoherence.Comment: I. F-G. Now publishes under name I. Fuentes-Schuller Published versio

VERY HIGH-RESOLUTION 3D SURVEYING AND MODELLING EXPERIENCES IN CIVIL ENGINEERING APPLICATIONS

In this paper some experiences in 3D modelling of objects with very high-resolution are described, carried out by the DICAM Geomatics group of the University of Bologna in multi-disciplinary contexts within the field of the Civil Engineering. In all the addressed case studies the main aim is the generation of a 3D model of the surface at a sub-millimetric scale, allowing a very accurate characterization of the surface geometry, useful for different purposes. 3D scanning and Structure from Motion photogrammetry have been used to generate the 3D models. In the paper the encountered problems and the adopted solutions in data surveying and processing are underlined, also discussing the added value of very high-resolution 3D modelling in multi-disciplinary activities

VERY HIGH-RESOLUTION 3D SURVEYING AND MODELLING EXPERIENCES IN CIVIL ENGINEERING APPLICATIONS

Abstract. In this paper some experiences in 3D modelling of objects with very high-resolution are described, carried out by the DICAM Geomatics group of the University of Bologna in multi-disciplinary contexts within the field of the Civil Engineering. In all the addressed case studies the main aim is the generation of a 3D model of the surface at a sub-millimetric scale, allowing a very accurate characterization of the surface geometry, useful for different purposes. 3D scanning and Structure from Motion photogrammetry have been used to generate the 3D models. In the paper the encountered problems and the adopted solutions in data surveying and processing are underlined, also discussing the added value of very high-resolution 3D modelling in multi-disciplinary activities

unconscious priming by illusory figures the role of the salient region

In this study we provide evidence that unconscious priming can be obtained as a result of the processing of the salient region (SR) of illusory figures and without that of illusory contours (ICs). We used a metacontrast masking paradigm where illusory figures were masked by real figures. In Experiment 1 we found a clear priming effect when participants were asked to discriminate between square and diamond masks preceded by congruent or incongruent illusory square or diamond primes. It is likely that metacontrast impairs the processing of ICs but not of the SR; therefore the above result strongly suggests that the priming effect was specifically related to the processing of the SR. In Experiment 2 participants were tested in the same task as in Experiment 1 with additional primes in which the inducers were presented in the same locations but their shapes were changed so as to modify the global configuration. We termed these primes High, Low, and No Salient Region (HSR, LSR, and NSR, respectively). The HSR condition replicated Experiment 1, whereas in the LSR and NSR conditions the priming effect got progressively smaller. The results of Experiment 1 were replicated with the priming effect significantly larger in the HSR than in all other conditions. It was also larger in the HSR than in LSR condition and smallest but still present in the NSR condition. Taken together, these results indicate that the unconscious processing of only the SR yields a priming effect and that a reduction of the saliency of the SR leads to a reduction of the priming effect, while its elimination does not abolish it

Noncommutative fluid dynamics in the Snyder space-time

In this paper, we construct for the first time the non-commutative fluid with the deformed Poincare invariance. To this end, the realization formalism of the noncommutative spaces is employed and the results are particularized to the Snyder space. The non-commutative fluid generalizes the fluid model in the action functional formulation to the noncommutative space. The fluid equations of motion and the conserved energy-momentum tensor are obtained.Comment: 12 pages. Version published by Phys. Rev.

An algebraic Birkhoff decomposition for the continuous renormalization group

This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated as a change of boundary condition for a differential equation, and an algebraic Birkhoff decomposition for rooted trees is explicited

Continuum spin foam model for 3d gravity

An example illustrating a continuum spin foam framework is presented. This covariant framework induces the kinematics of canonical loop quantization, and its dynamics is generated by a {\em renormalized} sum over colored polyhedra. Physically the example corresponds to 3d gravity with cosmological constant. Starting from a kinematical structure that accommodates local degrees of freedom and does not involve the choice of any background structure (e. g. triangulation), the dynamics reduces the field theory to have only global degrees of freedom. The result is {\em projectively} equivalent to the Turaev-Viro model.Comment: 12 pages, 3 figure

Historical Photogrammetry and Terrestrial Laser Scanning for the 3d Virtual Reconstruction of Destroyed Structures: a Case Study in Italy

The current dramatic episodes of destruction of archaeological sites have again highlighted the problem of the safeguarding the threatened heritage and, if possible, recovering those damaged by all the armed conflicts of the past. The historical photogrammetry offers the possibility to recover a posteriori the geometrical and material properties of destroyed structures, reconstructing their 3D model to document, study and maintain their memory, until to support their real anastylosis. The presented work is about the 3D reconstruction of the civic tower of the little town of Sant'Alberto, near the city of Ravenna, Italy. The tower, as a symbol of resistance and pride of the town's population, was destroyed in December 1944 by German troops in retaliation, when they were forced to leave the area. A city committee has subsequently collected all the historical evidence concerning the tower, including a series of photographic images that can be used for the photogrammetric reconstruction; the images calibration and orientation have been solved using the geometric information derived by a terrestrial laser scanner survey realized in the area where the tower was originally located. Despite the scarcity and very poor quality of the available images, the conducted photogrammetric procedure has allowed a complete and qualitatively satisfying object reconstruction, also thanks to the use of geometric constraint tools offered by the chosen software. The integration between the obtained model of the old tower and the 3D TLS survey of the square made it possible to reconstruct the ancient situation of the area

Differential structure on kappa-Minkowski space, and kappa-Poincare algebra

We construct realizations of the generators of the $\kappa$-Minkowski space and $\kappa$-Poincar\'{e} algebra as formal power series in the $h$-adic extension of the Weyl algebra. The Hopf algebra structure of the $\kappa$-Poincar\'{e} algebra related to different realizations is given. We construct realizations of the exterior derivative and one-forms, and define a differential calculus on $\kappa$-Minkowski space which is compatible with the action of the Lorentz algebra. In contrast to the conventional bicovariant calculus, the space of one-forms has the same dimension as the $\kappa$-Minkowski space.Comment: 20 pages. Accepted for publication in International Journal of Modern Physics