New Angle on the Strong CP and Chiral Symmetry Problems from a Rotating Mass Matrix

It is shown that when the mass matrix changes in orientation (rotates) in generation space for changing energy scale, then the masses of the lower generations are not given just by its eigenvalues. In particular, these masses need not be zero even when the eigenvalues are zero. In that case, the strong CP problem can be avoided by removing the unwanted $\theta$ term by a chiral transformation in no contradiction with the nonvanishing quark masses experimentally observed. Similarly, a rotating mass matrix may shed new light on the problem of chiral symmetry breaking. That the fermion mass matrix may so rotate with scale has been suggested before as a possible explanation for up-down fermion mixing and fermion mass hierarchy, giving results in good agreement with experiment.Comment: 14 page

Fermion Generations and Mixing from Dualized Standard Model

We review a possible solution to the fermion generation puzzle based on a nonabelian generalization of electric--magnetic duality derived some years ago. This nonabelian duality implies the existence of another SU(3) symmetry dual to colour, which is necessarily broken when colour is confined and so can play the role of the ``horizontal'' symmetry for fermion generations. When thus identified, dual colour then predicts 3 and only 3 fermion generations, besides suggesting a special Higgs mechanism for breaking the generation symmetry. A phenomenological model with a Higgs potential and a Yukawa coupling constructed on these premises is shown to explain immediately all the salient qualitative features of the fermion mass hierarchy and mixing pattern, excepting for the moment CP-violation. Calculations already carried out to 1-loop order is shown to give with only 3 adjustable parameters the following quantities all to within present experimental error: all 9 CKM matrix elements $|V_{rs}|$ for quarks, the neutrino oscillation angles or the MNS lepton mixing matrix elements $|U_{\mu 3}|, |U_{e 3}|$, and the mass ratios $m_c/m_t, m_s/m_b, m_\mu/m_\tau$. The special feature of this model crucial for deriving the above results is a fermion mass matrix which changes its orientation (rotates) in generation space with changing energy scale, a feature which is shown to have direct empirical support.Comment: updated version of course of lectures given at the 42nd Cracow School of Theoretical Physics, 2002, Polan

Doping Nanocrystals And The Role Of Quantum Confinement

Recent progress in developing algorithms for solving the electronic structure problem for nanostructures is illustrated. Key ingredients in this approach include pseudopotentials implemented on a real space grid and the use of density functional theory. This procedure allows one to predict electronic properties for many materials across the nano-regime, i.e., from atoms to nanocrystals of sufficient size to replicate bulk properties. We will illustrate this method for doping silicon nanocrystals with phosphorous.Institute for Computational Engineering and Sciences (ICES

Applications of physical methods in high-frequency futures markets

In the present work we demonstrate the application of different physical methods to high-frequency or tick-by-tick financial time series data. In particular, we calculate the Hurst exponent and inverse statistics for the price time series taken from a range of futures indices. Additionally, we show that in a limit order book the relaxation times of an imbalanced book state with more demand or supply can be described by stretched exponential laws analogous to those seen in many physical systems.Comment: 14 Pages and 10 figures. Proceeding to the SPIE conference, 4 - 7 December 2007 Australian National Univ. Canberra, ACT, Australi

A Model Behind the Standard Model

In spite of its many successes, the Standard Model makes many empirical assumptions in the Higgs and fermion sectors for which a deeper theoretical basis is sought. Starting from the usual gauge symmetry $u(1) \times su(2) \times su(3)$ plus the 3 assumptions: (A) scalar fields as vielbeins in internal symmetry space \cite{framevec}, (B) the ``confinement picture'' of symmetry breaking \cite{tHooft,Banovici}, (C) generations as ``dual'' to colour \cite{genmixdsm}, we are led to a scheme which offers: (I) a geometrical significance to scalar fields, (II) a theoretical criterion on what scalar fields are to be introduced, (III) a partial explanation of why $su(2)$ appears broken while $su(3)$ confines, (IV) baryon-lepton number (B - L) conservation, (V) the standard electroweak structure, (VI) a 3-valued generation index for leptons and quarks, and (VII) a dynamical system with all the essential features of an earlier phenomenological model \cite{genmixdsm} which gave a good description of the known mass and mixing patterns of quarks and leptons including neutrino oscillations. There are other implications the consistency of which with experiment, however, has not yet been systematically explored. A possible outcome is a whole new branch of particle spectroscopy from $su(2)$ confinement, potentially as rich in details as that of hadrons from colour confinement, which will be accessible to experiment at high energy.Comment: 66 pages, added new material on phenomenology, and some new reference

Entropy for Asymptotically AdS_3 Black Holes

We propose that Strominger's method to derive the BTZ black hole entropy is in fact applicable to other asymptotically AdS_3 black holes and gives the correct functional form of entropies. We discuss various solutions in the Einstein-Maxwell theory, dilaton gravity, Einstein-scalar theories, and Einstein-Maxwell-dilaton theory. In some cases, solutions approach AdS_3 asymptotically, but their entropies do not have the form of Cardy's formula. However, it turns out that they are actually not "asymptotically $AdS_3$" solutions. On the other hand, for truly asymptotically AdS_3 solutions, their entropies have the form of Cardy's formula. In this sense, all known solutions are consistent with our proposal.Comment: 21 pages, LaTeX; v2: added discussion for section 3.