Differential Entropy on Statistical Spaces

We show that the previously introduced concept of distance on statistical spaces leads to a straightforward definition of differential entropy on these statistical spaces. These spaces are characterized by the fact that their points can only be localized within a certain volume and exhibit thus a feature of fuzziness. This implies that Riemann integrability of relevant integrals is no longer secured. Some discussion on the specialization of this formalism to quantum states concludes the paper.Comment: 4 pages, to appear in the proceedings of the joint meeting of the 2nd International Conference on Cybernetics and Information Technologies, Systems and Applications (CITSA 2005) and the 11th International Conference on Information Systems Analysis and Synthesis (ISAS 2005), to be held in Orlando, USA, on July 14-17, 200

Metric on a Statistical Space-Time

We introduce a concept of distance for a space-time where the notion of point is replaced by the notion of physical states e.g. probability distributions. We apply ideas of information theory and compute the Fisher information matrix on such a space-time. This matrix is the metric on that manifold. We apply these ideas to a simple model and show that the Lorentzian metric can be obtained if we assumed that the probability distributions describing space-time fluctuations have complex values. Such complex probability distributions appear in non-Hermitian quantum mechanics.Comment: 7 page

Grand Unification on Noncommutative Spacetime

We compute the beta-functions of the standard model formulated on a noncommutative spacetime. If we assume that the scale for spacetime noncommutativity is of the order of 2.2 \times 10^{15} GeV we find that the three gauge couplings of the standard model merge at a scale of 2.3 \times 10^{17} GeV. The proton lifetime is thus much longer than in conventional unification models.Comment: 6 pages, published versio

Primordial Black Holes and a Large Hidden Sector

In this note we point out that primordial black holes could be much shorter lived than usually assumed if there is a large hidden sector of particles that only interacts gravitationally with the particles of the standard model. The observation of the explosion of one of these black holes would severely constrain the energy scale at which gravity becomes strong.Comment: 6 page

Asymptotically safe weak interactions

We emphasize that the electroweak interactions without a Higgs boson are very similar to quantum general relativity. The Higgs field could just be a dressing field and might not exist as a propagating particle. In that interpretation, the electroweak interactions without a Higgs boson could be renormalizable at the non-perturbative level because of a non-trivial fixed point. Tree-level unitarity in electroweak bosons scattering is restored by the running of the weak scale.Comment: 7 page

Yang-Mills Theories on Noncommutative Space-Time

We describe some recent progress in our understanding of Yang-Mills theories formulated on noncommutative spaces and in particular how to formulate the standard model on such spaces.Comment: To appear in the Proceedings of SUSY 2003, held at the University of Arizona, Tucson, AZ, 5-10 June 2003, 4 page

Radiative Lepton Decays and the Substructure of Leptons

The leptons are viewed as composite objects, exhibiting anomalous magnetic moments and anomalous flavor-changing transition moments. The decay \mu \to e \gamma is expected to occur with a branching ratio of the same order as the present experimental limit. The first order QED radiative correction is considered.Comment: 5 pages, to appear in the proceedings of the International Europhysics Conference on High Energy Physics, July 12-18 2001, Budapes

Equivalence principle and the gauge hierarchy problem

We show that the gauge hierarchy problem can be solved in the framework of scalar-tensor theories of gravity very much in the same way as it is solved in the Randall-Sundrum scenario. Our solution involves a fine-tuning of the gravitational sector which can, however, be avoided if a supergravity extension of the dilaton sector is considered. However our mechanism does not require the introduction of extra dimensions or new physics strongly coupled to the standard model in the low energy regime. We do introduce a new scalar field which is, however, coupled only gravitationally to regular matter. The physical reason for the splitting between the weak scale and the Planck scale is a violation of Einstein's equivalence principle

Gravitational Corrections to Fermion Masses in Grand Unified Theories

We reconsider quantum gravitational threshold effects to the unification of fermion masses in Grand Unified Theories. We show that the running of the Planck mass can have a sizable effect on these thresholds which are thus much more important than naively expected. These corrections make any extrapolation from low energy measurements challenging.Comment: 7 page

The Cosmological Evolution of the Nucleon Mass and the Electroweak Coupling Constants

Starting from astrophysical indications that the fine structure constant might undergo a small cosmological time shift, we discuss the implications of such an effect from the point of view of particle physics. Grand unification implies small time shifts for the nucleon mass, the magnetic moment of the nucleon and the weak coupling constant as well. The relative change of the nucleon mass is about 40 times larger than the relative change of alpha. Laboratory measurements using very advanced methods in quantum optics might soon reveal small time shifts of the nucleon mass, the magnetic moment of the nucleon and the fine structure constant.Comment: 4 page