Standing waves in the Lorentz-covariant world

When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is largely because of the emergence of quantum mechanics with wave-particle duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have to deal with Lorentz transformations of waves. We now have some understanding of plane waves or running waves in the covariant picture, but we do not yet have a clear picture of standing waves. In this report, we show that there is one set of standing waves which can be Lorentz-transformed while being consistent with all physical principle of quantum mechanics and relativity. It is possible to construct a representation of the Poincar\'e group using harmonic oscillator wave functions satisfying space-time boundary conditions. This set of wave functions is capable of explaining the quantum bound state for both slow and fast hadrons. In particular it can explain the quark model for hadrons at rest, and Feynman's parton model hadrons moving with a speed close to that of light.Comment: LaTex 20 pages, presented at the 2004 meeting of the International Association of Relativistic Dynamincs, to be published in the proceeding

Proton pygmy resonances: predictions for N=20 isotones

We study theoretically the low-energy electric-dipole response of N=20 isotones. We present results from a quasiparticle random-phase approximation (QRPA) and a continuum random-phase approximation (CRPA), and we compare them with results for the mirror Z=20 nuclei. According to our analysis, enhanced E1 strength is expected energetically well below the giant dipole resonance in the proton-rich isotones. Large amounts of E1 strength in the asymmetric N=20 isotones are predicted, unlike their equally asymmetric Z=20 mirror nuclei, pointing unambiguously to the role of structural effects such as loose binding. A proton-skin oscillation could develop especially in 46Fe. The proper description of non localized threshold transitions and the nucleon effective mass in mean-field treatments may affect theoretical predictions. We call for systematic theoretical investigations to quantify the role bulk-matter properties, in anticipation of measurements of E1 transitions in proton-rich nuclei.Comment: 10 pages, incl. 9 figures and 2 tables; v2: some rephrasing and clarifications, corrected Fig.

Coupled oscillators and Feynman's three papers

According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the ``rest of the universe'' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.Comment: 31 pages, 6 figures, based on the concluding talk at the 3rd Feynman Festival (Collage Park, Maryland, U.S.A., August 2006), minor correction

Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mapping

We consider the problem of estimating a sparse multi-response regression function, with an application to expression quantitative trait locus (eQTL) mapping, where the goal is to discover genetic variations that influence gene-expression levels. In particular, we investigate a shrinkage technique capable of capturing a given hierarchical structure over the responses, such as a hierarchical clustering tree with leaf nodes for responses and internal nodes for clusters of related responses at multiple granularity, and we seek to leverage this structure to recover covariates relevant to each hierarchically-defined cluster of responses. We propose a tree-guided group lasso, or tree lasso, for estimating such structured sparsity under multi-response regression by employing a novel penalty function constructed from the tree. We describe a systematic weighting scheme for the overlapping groups in the tree-penalty such that each regression coefficient is penalized in a balanced manner despite the inhomogeneous multiplicity of group memberships of the regression coefficients due to overlaps among groups. For efficient optimization, we employ a smoothing proximal gradient method that was originally developed for a general class of structured-sparsity-inducing penalties. Using simulated and yeast data sets, we demonstrate that our method shows a superior performance in terms of both prediction errors and recovery of true sparsity patterns, compared to other methods for learning a multivariate-response regression.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS549 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Feynman's Decoherence

Gell-Mann's quarks are coherent particles confined within a hadron at rest, but Feynman's partons are incoherent particles which constitute a hadron moving with a velocity close to that of light. It is widely believed that the quark model and the parton model are two different manifestations of the same covariant entity. If this is the case, the question arises whether the Lorentz boost destroys coherence. It is pointed out that this is not the case, and it is possible to resolve this puzzle without inventing new physics. It is shown that this decoherence is due to the measurement processes which are less than complete.Comment: RevTex 15 pages including 6 figs, presented at the 9th Int'l Conference on Quantum Optics (Raubichi, Belarus, May 2002), to be published in the proceeding

New Asymptotic Expanstion Method for the Wheeler-DeWitt Equation

A new asymptotic expansion method is developed to separate the Wheeler-DeWitt equation into the time-dependent Schr\"{o}dinger equation for a matter field and the Einstein-Hamilton-Jacobi equation for the gravitational field including the quantum back-reaction of the matter field. In particular, the nonadiabatic basis of the generalized invariant for the matter field Hamiltonian separates the Wheeler-DeWitt equation completely in the asymptotic limit of $m_p^2$ approaching infinity. The higher order quantum corrections of the gravity to the matter field are found. The new asymptotic expansion method is valid throughout all regions of superspace compared with other expansion methods with a certain limited region of validity. We apply the new asymptotic expansion method to the minimal FRW universe.Comment: 24 pages of Latex file, revte

The Role of executive function in children\u27s source monitoring with varying retrieval strategies

Previous research on the relationship between executive function and source monitoring in young children has been inconclusive, with studies finding conflicting results about whether working memory and inhibitory control are related to source-monitoring ability. In this study, the role of working memory and inhibitory control in recognition memory and source monitoring with two different retrieval strategies were examined. Children (N = 263) aged 4–8 participated in science activities with two sources. They were later given a recognition and source-monitoring test, and completed measures of working memory and inhibitory control. During the source-monitoring test, half of the participants were asked about sources serially (one after the other) whereas the other half of the children were asked about sources in parallel (considering both sources simultaneously). Results demonstrated that working memory was a predictor of source-monitoring accuracy in both conditions, but inhibitory control was only related to source accuracy in the parallel condition. When age was controlled these relationships were no longer significant, suggesting that a more general cognitive development factor is a stronger predictor of source monitoring than executive function alone. Interestingly, the children aged 4–6 years made more accurate source decisions in the parallel condition than in the serial condition. The older children (aged 7–8) were overall more accurate than the younger children, and their accuracy did not differ as a function of interview condition. Suggestions are provided to guide further research in this area that will clarify the diverse results of previous studies examining whether executive function is a cognitive prerequisite for effective source monitoring