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

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

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

Seesaw induced Higgs Mechanism

We discuss a two scalar doublets model which induces the Higgs mechanism by means of a seesaw mechanism. This model naturally predicts a light Higgs scalar whose mass is suppressed by the grand unification scale. The model predicts an intermediate scale between the electroweak symmetry breaking scale and the grand unification scale at $10^9$ GeV. Below this intermediate energy scale the usual standard model appears as an effective theory. A seesaw mechanism in the scalar sector of the model not only induces the standard Higgs mechanism, but also solves the hierarchy problem. An implementation of this mechanism in models where the Planck scale is in the TeV region is discussed.Comment: 4 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

Minimal Grand Unification Model in an Anthropic Landscape

It has been recently pointed out by Arkani-Hamed and Dimopoulos that if the universe is a landscape of vacua, and if therefore fine-tuning is not a valid guidance principle for searching for physics beyond the standard model, supersymmetric unification only requires the fermionic superpartners. We argue that in that landscape scenario, the fermionic superpartners are not needed for unification, which can be achieved in SO(10) either via a direct breaking to the standard model at the grand unification scale or through an intermediate gauge symmetry. In most minimal SO(10) models, the proton lifetime is long enough to avoid the experimental bounds. These models are the truly minimal fine-tuned extensions of the standard model in the sense proposed by Davoudiasl et al..Comment: 11 page

Quantum Mechanics on Noncommutative Spacetime

We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note however that noncommutative intrinsic dipole moments are not observable in present experiments searching for an EDM of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moment are thus incorrect.Comment: 8 page

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

Grand Unification and Time Variation of the Gauge Couplings

Astrophysical indications that the fine structure constant is time dependent are discussed in the framework of grand unification models. A variation of the electromagnetic coupling constant could either be generated by a corresponding time variation of the unified coupling constant or by a time variation of the unification scale, or by both. The case in which the time variation of the electromagnetic coupling constant is caused by a time variation of the unification scale is of special interest. It is supported in addition by recent hints towards a time change of the proton-electron mass ratio. Possible implications for baryogenesis are discussed.Comment: talk given at the 10th International Conference on Supersymmetry and Unification of Fundamental Interactions (SUSY02), Hamburg, Germany, 17-23 June 200

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