27,985 research outputs found
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 -boson -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
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