Gauge-variant propagators and the running coupling from lattice QCD

On the occasion of the 70th birthday of Prof. Adriano Di Giacomo we report on recent numerical computations of the Landau gauge gluon and ghost propagators as well as of a non-symmetric MOM-scheme ghost-gluon vertex in quenched and full lattice QCD. Special emphasis is paid to the Gribov copy problem and to the unquenching effect. The corresponding running coupling \alpha_s(q^2) is found and shown to decrease for q^2 \le 0.3 GeV^2 in the infrared limit. No indication for a non-trivial infrared fixed point is seen in agreement with findings from truncated systems of Dyson-Schwinger equations treated on a four-dimensional torus.Comment: contribution to "Sense of Beauty in Physics", Festschrift in honor of Adriano Di Giacomo's 70-th birthda

Gravitational waves and fundamental physics

I give an overview of the motivations for gravitational-wave research, concentrating on the aspects related to ``fundamental'' physics.Comment: 12 pages, 2 figures, to appear in "Sense of Beauty in Physics", a Volume in honour of the 70th birthday of Adriano Di Giacom

Topology on the Lattice

We review the method developed in Pisa to determine the topological susceptibility in lattice QCD and present a collection of new and old results obtained by the method.Comment: 10 pages, 7 figures. Contribution to "Sense of Beauty in Physics - a volume in honour of Adriano Di Giacomo" (Pisa University Press, Pisa, 2006), on the occasion of his 70th birthda

Charm and Beauty in a Hot Environment

We discuss the spectral analysis of quarkonium states in a hot medium of deconfined quarks and gluons, and we show that such an analysis provides a way to determine the thermal properties of the quark-gluon plasma.Comment: 14 pages, 15 figures; presented at the meeting "A Sense of Beauty in Physics", honoring the 70th birthday of Adriano Di Giacomo; Pisa, Jan. 26 -27, 200

Boundary State for Magnetized D9 Branes and One-Loop Calculation

We construct the boundary state describing magnetized D9 branes in R^{3,1} x T^6 and we use it to compute the annulus and Moebius amplitudes. We derive from them, by using open/closed string duality, the number of Landau levels on the torus T^d.Comment: 12 pages,in honor of Adriano Di Giacomo on his 70th birthday, contribution to the Festschrif

Non-Symmetric Hall-Littlewood Polynomials

Using the action of the Yang-Baxter elements of the Hecke algebra on polynomials, we define two bases of polynomials in n variables. The Hall-Littlewood polynomials are a subfamily of one of them. For q=0, these bases specialize into the two families of classical Key polynomials (i.e. Demazure characters for type A). We give a scalar product for which the two bases are adjoint of each other.Comment: Dedicated to Adriano Garsi