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

The algebraic structure of the generalized uncertainty principle

We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter $\kappa$ is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity. The deformed algebra and therefore the form of the generalized uncertainty principle are fixed uniquely by rather simple assumptions. The string theory result is reproduced expanding our result at first order in $\Delta p/M_{\rm PL}$. We also briefly comment on possible implications for Lorentz invariance at the Planck scale.Comment: 6 pages, IFUP-TH 38/9

Algebraic renormalization of N=2 Super Yang-Mills theories coupled to matter

We study the algebraic renormalization of $N=2$ Supersymmetric Yang--Mills theories coupled to matter. A regularization procedure preserving both the BRS invariance and the supersymmetry is not known yet, therefore it is necessary to adopt the algebraic method of renormalization, which does not rely on any regularization scheme. The whole analysis is reduced to the solution of cohomology problems arising from the generalized Slavnov operator which summarizes all the symmetries of the model. Besides to unphysical renormalizations of the quantum fields, we find that the only coupling constant of $N=2$ SYMs can get quantum corrections. Moreover we prove that all the symmetries defining the theory are algebraically anomaly--free.Comment: typing error in eq. (A.9) correcte