Cabled Wilson Loops in BF Theories

A generating function for cabled Wilson loops in three-dimensional BF theories is defined, and a careful study of its behavior for vanishing cosmological constant is performed. This allows an exhaustive description of the unframed knot invariants coming from the pure BF theory based on SU(2), and in particular, it proves a conjecture relating them to the Alexander-Conway polynomial.Comment: 30 pages, LaTe

Configuration space integrals and invariants for 3-manifolds and knots

The first part of this paper is a short review of the construction [dg-ga/9710001] of invariants of rational homology 3-spheres and knots in terms of configuration space integrals. The second part describes the relationship between the above construction and Kontsevich's proposal of removing one point from the rational homology sphere. Explicit formulae are computed. In the case of the "Theta" invariant, a comparison with Taubes's construction is briefly discussed.Comment: 17 pages, AMS-LaTeX; proceedings of the Madeira conference on "Low Dimensional Topology," January 199

Deformation Quantization and Reduction

This note is an overview of the Poisson sigma model (PSM) and its applications in deformation quantization. Reduction of coisotropic and pre-Poisson submanifolds, their appearance as branes of the PSM, quantization in terms of L-infinity and A-infinity algebras, and bimodule structures are recalled. As an application, an "almost" functorial quantization of Poisson maps is presented if no anomalies occur. This leads in principle to a novel approach for the quantization of Poisson-Lie groups.Comment: 23 pages, 3 figures; added references, corrected typo

Galilean currents and charges

We derive the Noether currents and charges associated with an internal galilean invariance---a symmetry recently postulated in the context of so-called galileon theories. Along the way we clarify the physical interpretation of the Noether charges associated with ordinary Galileo- and Lorentz-boosts.Comment: 5 page

Wave relations

The wave equation (free boson) problem is studied from the viewpoint of the relations on the symplectic manifolds associated to the boundary induced by solutions. Unexpectedly there is still something to say on this simple, well-studied problem. In particular, boundaries which do not allow for a meaningful Hamiltonian evolution are not problematic from the viewpoint of relations. In the two-dimensional Minkowski case, these relations are shown to be Lagrangian. This result is then extended to a wide class of metrics and is conjectured to be true also in higher dimensions for nice enough metrics. A counterexample where the relation is not Lagrangian is provided by the Misner space.Comment: 27 pages; minor clarifying changes added; to appear in CM

Pre-Poisson submanifolds

This is an expository and introductory note on some results obtained in "Coisotropic embeddings in Poisson manifolds" (ArXiv math/0611480). Some original material is contained in the last two sections, where we consider linear Poisson structures.Comment: Proceedings of the conference "Poisson 2006". 14 page

Scale Evolution of Unintegrated Distributions and the p_t Spectrum of Gauge Bosons

We present predictions for the $Z$-boson $p_t$-spectrum at Tevatron within the framework of unintegrated distributions evolved according to evolution equations recently proposed by us. We discuss the dependence of the results on the choice of non-perturbative parameters, the coupling constant and the impact of soft gluon resummation.Comment: proceedings of the workshop "Recent Advances in Perturbative QCD and Hadronic Physics", 20-25 July 2009, ECT*, Trento (Italy), in Honor of Prof. Anatoly Efremov's 75th Birthday Celebratio

Formality and Star Products

These notes, based on the mini-course given at the PQR2003 Euroschool held in Brussels in 2003, aim to review Kontsevich's formality theorem together with his formula for the star product on a given Poisson manifold. A brief introduction to the employed mathematical tools and physical motivations is also given.Comment: 49 pages, 9 figures; proceedings of the PQR2003 Euroschool. Version 2 has minor correction

Explosive synchronization with partial degree-frequency correlation

Networks of Kuramoto oscillators with a positive correlation between the oscillators frequencies and the degree of the their corresponding vertices exhibits the so-called explosive synchronization behavior, which is now under intensive investigation. Here, we study and report explosive synchronization in a situation that has not yet been considered, namely when only a part, typically small, of the vertices is subjected to a degree frequency correlation. Our results show that in order to have explosive synchronization, it suffices to have degree-frequency correlations only for the hubs, the vertices with the highest degrees. Moreover, we show that a partial degree-frequency correlation does not only promotes but also allows explosive synchronization to happen in networks for which a full degree-frequency correlation would not allow it. We perform exhaustive numerical experiments for synthetic networks and also for the undirected and unweighted version of the neural network of the worm Caenorhabditis elegans. The latter is an explicit example where partial degree-frequency correlation leads to explosive synchronization with hysteresis, in contrast with the fully correlated case, for which no explosive synchronization is observed.Comment: 10 pages, 6 figures, final version to appear in PR