Unitarity, ghosts and nonminimal terms in Lorentz violating QED

The unitarity of a Lorentz-invariance violating QED model with higher-order Myers and Pospelov photons coupled to standard fermions is studied. As expected, we find ghost states associated to the higher-order terms that may lead to the loss of unitarity. An explicit calculation to check perturbative unitarity in the process of electron-positron scattering is performed and it is found to be possible to be preserved.Comment: Presented at the Sixth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 17-21, 201

Field theory approach to one-dimensional electronic systems

In this talk I describe a recently introduced field-theoretical approach that can be used as an alternative framework to study one-dimensional systems of highly correlated particles.Comment: 25 pages, latex, no figures. Talk delivered at Trends in Theoretical Physics - CERN - Santiago de Compostela - La Plata Meeting, La Plata, April-May 1997, to be published. Abstract modifie

Numerical solution of conservative finite-dimensional stochastic Schrodinger equations

The paper deals with the numerical solution of the nonlinear Ito stochastic differential equations (SDEs) appearing in the unravelling of quantum master equations. We first develop an exponential scheme of weak order 1 for general globally Lipschitz SDEs governed by Brownian motions. Then, we proceed to study the numerical integration of a class of locally Lipschitz SDEs. More precisely, we adapt the exponential scheme obtained in the first part of the work to the characteristics of certain finite-dimensional nonlinear stochastic Schrodinger equations. This yields a numerical method for the simulation of the mean value of quantum observables. We address the rate of convergence arising in this computation. Finally, an experiment with a representative quantum master equation illustrates the good performance of the new scheme.Comment: Published at http://dx.doi.org/10.1214/105051605000000403 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Tractable State-Space Model for Symmetric Positive-Definite Matrices

Bayesian analysis of state-space models includes computing the posterior distribution of the system's parameters as well as filtering, smoothing, and predicting the system's latent states. When the latent states wander around $\mathbb{R}^n$ there are several well-known modeling components and computational tools that may be profitably combined to achieve these tasks. However, there are scenarios, like tracking an object in a video or tracking a covariance matrix of financial assets returns, when the latent states are restricted to a curve within $\mathbb{R}^n$ and these models and tools do not immediately apply. Within this constrained setting, most work has focused on filtering and less attention has been paid to the other aspects of Bayesian state-space inference, which tend to be more challenging. To that end, we present a state-space model whose latent states take values on the manifold of symmetric positive-definite matrices and for which one may easily compute the posterior distribution of the latent states and the system's parameters, in addition to filtered distributions and one-step ahead predictions. Deploying the model within the context of finance, we show how one can use realized covariance matrices as data to predict latent time-varying covariance matrices. This approach out-performs factor stochastic volatility.Comment: 22 pages: 16 pages main manuscript, 4 pages appendix, 2 pages reference

Immigrant Heterogeneity and the Earnings Distribution in the United Kingdom and United States: New Evidence from a Panel Data Quantile Regression Analysis

In this paper we use a relatively new panel data quantile regression technique to examine native-immigrant earnings differentials 1) throughout the conditional wage distribution, and 2) controlling for individual heterogeneity. No previous papers have simultaneously considered these factors. We focus on both women and men, using longitudinal data from the PSID and the BHPS. We show that country of origin, country of residence, and gender are all important deter- minants of the earnings differential. For instance, a large wage penalty occurs in the U.S. among female immigrants from non-English speaking countries, and the penalty is most negative among the lowest (conditional) wages. On the other hand, women in Britain experience hardly any immigrant-native wage differential. We find evidence suggesting that immigrant men in the U.S. and the U.K. earn lower wages, but the most significant results are found for British workers emigrating from non-English speaking countries. The various differentials we report in this paper reveal the value of combining quantile regression with controls for individual heterogeneity in better understanding immigrant wage effects