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

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

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

Sonographic Wrist Measurements and Detection of Anatomical Features in Carpal Tunnel Syndrome

INTRODUCTION: This study compares anatomical findings at wrist level in patients with known carpal tunnel syndrome (CTS) and controls by ultrasonography (US). MATERIAL AND METHODS: Wrist-US investigations of 28 consecutive patients with 38 diagnosed, idiopathic CTS were compared to 49 healthy volunteers without history of CTS. Internal wrists dimensions, the presence of flexor muscle bellies in the carpal tunnel, and cross-sectional area of the median nerve were analyzed. The findings were correlated to gender, age, and BMI. RESULTS: US demonstrated a square internal carpal tunnel configuration in CTS patients compared to controls (P < 0.001). Patients with CTS showed a trend towards the presence of flexor muscles bellies in the carpal tunnel (odds ratio 1.77, 95% CI 0.337-8.33). CTS was present in women with higher BMI (P = 0.015). CONCLUSION: US allowed detection of specific anatomical features at wrist level in CTS patients. This observation may enable--following confirmation in larger prospective studies--risk evaluation for CTS development

The tax identity for Markov additive risk processes

Taxed risk processes, i.e. processes which change their drift when reaching new maxima, represent a certain type of generalizations of Lévy and of Markov additive processes (MAP), since the times at which their Markovian mechanism changes are allowed to depend on the current position. In this paper we study generalizations of the tax identity of Albrecher and Hipp (2007) from the classical risk model to more general risk processes driven by spectrally-negative MAPs. We use the Sparre Andersen risk processes with phase-type interarrivals to illustrate the ideas in their simplest form