Quantization of the scalar field in a static quantum metric

We investigate the Hamiltonian formulation of quantum scalar fields in a static quantum metric. We derive a functional integral formula for the propagator. We show that the quantum metric substantially changes the behaviour of the scalar propagator and the effective Yukawa potential.Comment: Latex, 12 page

Towards a Simulation of Quantum Computers by Classical Systems

We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the Schroedinger equation of a harmonic oscillator. In this way we derive the discrete oscillator spectrum from classical dynamics. The model is then generalized to an arbitrary potential. This opens up the possibility of efficiently simulating quantum computers with the help of classical systems.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all PS fonts) at http://www.physik.fu-berlin.de/~kleinert/kleiner_re324/preprint.htm

Minimal gauge-Higgs unification with a flavour symmetry

We show that a flavour symmetry a la Froggatt-Nielsen can be naturally incorporated in models with gauge-Higgs unification, by exploiting the heavy fermions that are anyhow needed to realize realistic Yukawa couplings. The case of the minimal five-dimensional model, in which the SU(2)_L x U(1)_Y electroweak group is enlarged to an SU(3)_W group, and then broken to U(1)_em by the combination of an orbifold projection and a Scherk-Schwarz twist, is studied in detail. We show that the minimal way of incorporating a U(1)_F flavour symmetry is to enlarge it to an SU(2)_F group, which is then completely broken by the same orbifold projection and Scherk-Schwarz twist. The general features of this construction, where ordinary fermions live on the branes defined by the orbifold fixed-points and messenger fermions live in the bulk, are compared to those of ordinary four-dimensional flavour models, and some explicit examples are constructed.Comment: LaTex, 37 pages, 2 figures; some clarifying comments and a few references adde

Anarchy and Hierarchy

We advocate a new approach to study models of fermion masses and mixings, namely anarchy proposed in hep-ph/9911341. In this approach, we scan the O(1) coefficients randomly. We argue that this is the correct approach when the fundamental theory is sufficiently complicated. Assuming there is no physical distinction among three generations of neutrinos, the probability distributions in MNS mixing angles can be predicted independent of the choice of the measure. This is because the mixing angles are distributed according to the Haar measure of the Lie groups whose elements diagonalize the mass matrices. The near-maximal mixings, as observed in the atmospheric neutrino data and as required in the LMA solution to the solar neutrino problem, are highly probable. A small hierarchy between the Delta m^2 for the atmospheric and the solar neutrinos is obtained very easily; the complex seesaw case gives a hierarchy of a factor of 20 as the most probable one, even though this conclusion is more measure-dependent. U_{e3} has to be just below the current limit from the CHOOZ experiment. The CP-violating parameter sin delta is preferred to be maximal. We present a simple SU(5)-like extension of anarchy to the charged-lepton and quark sectors which works well phenomenologically.Comment: 26 page

A kinetic theory of diffusion in general relativity with cosmological scalar field

A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It is shown that the energy-momentum tensor for this matter model is not divergence-free, which makes it inconsistent to couple the Fokker-Planck equation to the Einstein equations. This problem can be solved by postulating the existence of additional matter fields in spacetime or by modifying the Einstein equations. The case of a cosmological scalar field term added to the left hand side of the Einstein equations is studied in some details. For the simplest cosmological model, namely the flat Robertson-Walker spacetime, it is shown that, depending on the initial value of the cosmological scalar field, which can be identified with the present observed value of the cosmological constant, either unlimited expansion or the formation of a singularity in finite time will occur in the future. Future collapse into a singularity also takes place for a suitable small but positive present value of the cosmological constant, in contrast to the standard diffusion-free scenario.Comment: 17 pages, no figures. The present version corrects an erroneous statement on the physical interpretation of the results made in the original publicatio