Supersymmetric Canonical Commutation Relations

We present unitarily represented supersymmetric canonical commutation relations which are subsequently used to canonically quantize massive and massless chiral,antichiral and vector fields. The massless fields, especially the vector one, show new facets which do not appear in the non superymmetric case. Our tool is the supersymmetric positivity induced by the Hilbert-Krein structure of the superspace.Comment: 14 page

Natural Metric for Quantum Information Theory

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation with other distances is investigated. As an illustrative application, the proposed metric is evaluated for 1-qubit mixed states.Comment: v2: enlarged; presented at ISIT 2008 (Toronto

Supersymmetric Distributions, Hilbert Spaces of Supersymmetric Functions and Quantum Fields

The recently investigated Hilbert-Krein and other positivity structures of the superspace are considered in the framework of superdistributions. These tools are applied to problems raised by the rigorous supersymmetric quantum field theory.Comment: 24 page

Van der Waerden calculus with commuting spinor variables and the Hilbert-Krein structure of the superspace

Working with anticommuting Weyl(or Mayorana) spinors in the framework of the van der Waerden calculus is standard in supersymmetry. The natural frame for rigorous supersymmetric quantum field theory makes use of operator-valued superdistributions defined on supersymmetric test functions. In turn this makes necessary a van der Waerden calculus in which the Grassmann variables anticommute but the fermionic components are commutative instead of being anticommutative. We work out such a calculus in view of applications to the rigorous conceptual problems of the N=1 supersymmetric quantum field theory.Comment: 14 page

BRST-anti-BRST Antifield formalism : The Example of the Freedman-Townsend Model

The general BRST-anti-BRST construction in the framework of the antifield-antibracket formalism is illustrated in the case of the Freedmann-Townsend model.Comment: 16 pages, Latex file, Latex errors corrected, otherwise unchange

Recurrence relation for relativistic atomic matrix elements

Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non relativistic quantum mechanics. We obtain first the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use such relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.Comment: 10 pages, no figure

Coordinate based random effect size meta-analysis of neuroimaging studies

Low power in neuroimaging studies can make them difficult to interpret, and Coordinate based meta-analysis (CBMA) may go some way to mitigating this issue. CBMA has been used in many analyses to detect where published functional MRI or voxel-based morphometry studies testing similar hypotheses report significant summary results (coordinates) consistently. Only the reported coordinates and possibly t statistics are analysed, and statistical significance of clusters is determined by coordinate density. Here a method of performing coordinate based random effect size meta-analysis and meta-regression is introduced. The algorithm (ClusterZ) analyses both coordinates and reported t statistic or Z score, standardised by the number of subjects. Statistical significance is determined not by coordinate density, but by a random effects meta-analyses of reported effects performed cluster-wise using standard statistical methods and taking account of censoring inherent in the published summary results. Type 1 error control is achieved using the false cluster discovery rate (FCDR), which is based on the false discovery rate. This controls both the family wise error rate under the null hypothesis that coordinates are randomly drawn from a standard stereotaxic space, and the proportion of significant clusters that are expected under the null. Such control is necessary to avoid propagating and even amplifying the very issues motivating the meta-analysis in the first place. ClusterZ is demonstrated on both numerically simulated data and on real data from reports of grey matter loss in multiple sclerosis (MS) and syndromes suggestive of MS, and of painful stimulus in healthy controls. The software implementation is available to download and use freely

Relativistically extended Blanchard recurrence relation for hydrogenic matrix elements

General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schr\"odinger case. A relativistic version of the Pasternack-Sternheimer relation is thence obtained in the diagonal (i.e. total angular momentum and parity the same) case, from such relation an expression for the relativistic virial theorem is deduced. To contribute to the utility of the relations, explicit expressions for the radial matrix elements of functions of the form $r^\lambda$ and $\beta r^\lambda$ ---where $\beta$ is a Dirac matrix--- are presented.Comment: 21 pages, to be published in J. Phys. B: At. Mol. Opt. Phys. in Apri