Where do bosons actually belong?

We explore a variety of reasons for considering su(1,1) instead of the customary h(1) as the natural unifying frame for characterizing boson systems. Resorting to the Lie-Hopf structure of these algebras, that shows how the Bose-Einstein statistics for identical bosons is correctly given in the su(1,1) framework, we prove that quantization of Maxwell's equations leads to su(1,1), relativistic covariance being naturally recognized as an internal symmetry of this dynamical algebra. Moreover su(1,1) rather than h(1) coordinates are associated to circularly polarized electromagnetic waves. As for interacting bosons, the su(1,1) formulation of the Jaynes-Cummings model is discussed, showing its advantages over h(1).Comment: 9 pages, to appear in J. Phys. A: Math. Theo

Spin network setting of topological quantum computation

The spin network simulator model represents a bridge between (generalised) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFTs). The key tool is provided by the fiber space structure underlying the model which exhibits combinatorial properties closely related to SU(2) state sum models, widely employed in discretizing TQFTs and quantum gravity in low spacetime dimensions.Comment: Proc. "Foundations of Quantum Information", Camerino (Italy), 16-19 April 2004, to be published in Int. J. of Quantum Informatio

Entropy estimates for Simplicial Quantum Gravity

Through techniques of controlled topology we determine the entropy function characterizing the distribution of combinatorially inequivalent metric ball coverings of n-dimensional manifolds of bounded geometry for every n ≥ 2. Such functions control the asymptotic distribution of dynamical triangulations of the corresponding n-dimensional (pseudo)manifolds M of bounded geometry. They have an exponential leading behavior determined by the Reidemeister-Franz torsion associated with orthogonal representations of the fundamental group of the manifold. The subleading terms are instead controlled by the Euler characteristic of M. Such results are either consistent with the known asymptotics of dynamically triangulated two-dimensional surfaces, or with the numerical evidence supporting an exponential leading behavior for the number of inequivalent dynamical triangulations on three- and four-dimensional manifolds

Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials

Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schroedinger-like equation which provides a semiclassical Hamiltonian picture of the evolution of a `quantum of space', as shown by the authors in a recent paper. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed.Comment: 10 pages, talk given at "Physics and Mathematics of Nonlinear Phenomena" (PMNP2013), to appear in J. Phys. Conf. Serie

The geometry of dynamical triangulations

We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume behavior. In the space of the coupling constants of the theory, we characterize the infinite volume line and the associated critical points. The results of this analysis are found to be in excellent agreement with the MonteCarlo simulations of simplicial quantum gravity. In particular, we provide an analytical proof that simply-connected dynamically triangulated 4-manifolds undergo a higher order phase transition at a value of the inverse gravitational coupling given by 1.387, and that the nature of this transition can be concealed by a bystable behavior. A similar analysis in the 3-dimensional case characterizes a value of the critical coupling (3.845) at which hysteresis effects are present.Comment: 166 pages, Revtex (latex) fil

Combinatorial and topological phase structure of non-perturbative n-dimensional quantum gravity

We provide a non-perturbative geometrical characterization of the partition function of $n$-dimensional quantum gravity based on a coarse classification of riemannian geometries. We show that, under natural geometrical constraints, the theory admits a continuum limit with a non-trivial phase structure parametrized by the homotopy types of the class of manifolds considered. The results obtained qualitatively coincide, when specialized to dimension two, with those of two-dimensional quantum gravity models based on random triangulations of surfaces.Comment: 13 page

Using Ground Transportation for Aviation System Disruption Alleviation

An investigation was made into whether passenger delays and airline costs due to disruptive events affecting European airports could be reduced by a coordinated strategy of using alternative flights and ground transportation to help stranded passengers reach their final destination using airport collaborative decision-making concepts. Optimizing for airline cost for hypothetical disruptive events suggests that, for airport closures of up to 10 h, airlines could benefit from up to a 20% reduction in passenger delay-related costs. The mean passenger delay could be reduced by up to 70%, mainly via a reduction in very long delays

Implementing holographic projections in Ponzano--Regge gravity

We consider the path-sum of Ponzano-Regge with additional boundary contributions in the context of the holographic principle of Quantum Gravity. We calculate an holographic projection in which the bulk partition function goes to a semi-classical limit while the boundary state functional remains quantum-mechanical. The properties of the resulting boundary theory are discussed.Comment: 20 pages, late