Hamilton-Jacobi Theory and Information Geometry

Recently, a method to dynamically define a divergence function $D$ for a given statistical manifold $(\mathcal{M}\,,g\,,T)$ by means of the Hamilton-Jacobi theory associated with a suitable Lagrangian function $\mathfrak{L}$ on $T\mathcal{M}$ has been proposed. Here we will review this construction and lay the basis for an inverse problem where we assume the divergence function $D$ to be known and we look for a Lagrangian function $\mathfrak{L}$ for which $D$ is a complete solution of the associated Hamilton-Jacobi theory. To apply these ideas to quantum systems, we have to replace probability distributions with probability amplitudes.Comment: 8 page

Model of the Quark Mixing Matrix

The structure of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is analyzed from the standpoint of a composite model. A model is constructed with three families of quarks, by taking tensor products of sufficient numbers of spin-1/2 representations and imagining the dominant terms in the mass matrix to arise from spin-spin interactions. Generic results then obtained include the familiar relation $|V_{us}| = (m_d/m_s)^{1/2} - (m_u/m_c)^{1/2}$, and a less frequently seen relation $|V_{cb}| = \sqrt{2} [(m_s/m_b) - (m_c/m_t)]$. The magnitudes of $V_{ub}$ and $V_{td}$ come out naturally to be of the right order. The phase in the CKM matrix can be put in by hand, but its origin remains obscure.Comment: Presented by Mihir P. Worah at DPF 92 Meeting, Fermilab, November, 1992. 3 pages, LaTeX fil

An Extended Technicolor Model

An extended technicolor model is constructed. Quark and lepton masses, spontaneous CP violation, and precision electroweak measurements are discussed. Dynamical symmetry breaking is analyzed using the concept of the BIG MAC.Comment: 35 pages, Latex, YCTP-P21-93, BUHEP-93-2

On classical finite and affine W-algebras

This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.Comment: 12 page

The Effective Electroweak Chiral Lagrangian: The Matter Sector

We parametrize in a model-independent way possible departures from the minimal Standard Model predictions in the matter sector. We only assume the symmetry breaking pattern of the Standard Model and that new particles are sufficiently heavy so that the symmetry is non-linearly realized. Models with dynamical symmetry breaking are generically of this type. We review in the effective theory language to what extent the simplest models of dynamical breaking are actually constrained and the assumptions going into the comparison with experiment. Dynamical symmetry breaking models can be approximated at intermediate energies by four-fermion operators. We present a complete classification of the latter when new particles appear in the usual representations of the $SU(2)_L\times SU(3)_c$ group as well as a partial classification in the general case. We discuss the accuracy of the four-fermion description by matching to a simple `fundamental' theory. The coefficients of the effective lagrangian in the matter sector for dynamical symmetry breaking models (expressed in terms of the coefficients of the four-quark operators) are then compared to those of models with elementary scalars (such as the minimal Standard Model). Contrary to a somewhat widespread belief, we see that the sign of the vertex corrections is not fixed in dynamical symmetry breaking models. This work provides the theoretical tools required to analyze, in a rather general setting, constraints on the matter sector of the Standard Model.Comment: Latex, 45 pages, 8 eps figures. Sections 5, 6 and 9 have been rewritten to clarify the contents. Some mistakes and typos have been corrected. Two references have been added. Figures 7 and 8 have been modifie

On extending actions of groups

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications

Phase-plate electron microscopy: a novel imaging tool to reveal close-to-life nano-structures

After slow progress in the efforts to develop phase plates for electron microscopes, functional phase plate using thin carbon film has been reported recently. It permits collecting high-contrast images of close-to-life biological structures with cryo-fixation and without staining. This report reviews the state of the art for phase plates and what is innovated with them in biological electron microscopy. The extension of thin-film phase plates to the material-less type using electrostatic field or magnetic field is also addressed

Seismogenic zone structure of the southern Middle America Trench, Costa Rica

The shallow seismogenic portion of subduction zones generates damaging large and great earthquakes. This study provides structural constraints on the seismogenic zone of the Middle America Trench offshore central Costa Rica and insights into the physical and mechanical characteristics controlling seismogenesis. We have located ~300 events that occurred following the MW 6.9, 20 August 1999, Quepos, Costa Rica, underthrusting earthquake using a three-dimensional velocity model and arrival time data recorded by a temporary local network of land and ocean bottom seismometers. We use aftershock locations to define the geometry and characteristics of the seismogenic zone in this region. These events define a plane dipping at 19° that marks the interface between the Cocos Plate and the Panama Block. The majority of aftershocks occur below 10 km and above 30 km depth below sea level, corresponding to 30–35 km and 95 km from the trench axis, respectively. Relative event relocation produces a seismicity pattern similar to that obtained using absolute locations, increasing confidence in the geometry of the seismogenic zone. The aftershock locations spatially correlate with the downdip extension of the oceanic Quepos Plateau and reflect the structure of the main shock rupture asperity. This strengthens an earlier argument that the 1999 Quepos earthquake ruptured specific bathymetric highs on the downgoing plate. We believe that subduction of this highly disrupted seafloor has established a set of conditions which presently limit the seismogenic zone to be between 10 and 35 km below sea level

Analysis of techni-dilaton as a dark matter candidate

The almost conformal dynamics of walking technicolor (TC) implies the existence of the approximate scale invariance, which breaks down spontaneously by the condensation of anti-techni and techni-fermions. According to the Goldstone theorem, a spinless, parity-even particle, called techni-dilaton (TD), then emerges at low energy. If TC exhibits an extreme walking, TD mass is parametrically much smaller than that of techni-fermions (around 1 TeV), while its decay constant is comparable to the cutoff scale of walking TC. We analyze the light, decoupled TD as a dark matter candidate and study cosmological productions of TD, both thermal and non-thermal, in the early Universe. The thermal population is governed dominantly by single TD production processes involving vertices breaking the scale symmetry, while the non-thermal population is by the vacuum misalignment and is accumulated via harmonic and coherent oscillations of misaligned classical TD fields. The non-thermal population turns out to be dominant and large enough to explain the abundance of presently observed dark matter, while the thermal population is highly suppressed due to the large TD decay constant. Several cosmological and astrophysical limits on the light, decoupled TD are examined to find that the TD mass is constrained to be in a range between 0.01 eV and 500 eV. From the combined constraints on cosmological productions and astrophysical observations, we find that the light, decoupled TD can be a good dark matter candidate with the mass around a few hundreds of eV for typical models of (extreme) walking TC. We finally mention possible designated experiments to detect the TD dark matter.Comment: 26 pages. 16 figures; v2, expanded Section 2.4 on composite Higgs in light of newly discovered Higgs-like particle at LH