Polymer quantization of the free scalar field and its classical limit

Building on prior work, a generally covariant reformulation of free scalar field theory on the flat Lorentzian cylinder is quantized using Loop Quantum Gravity (LQG) type `polymer' representations. This quantization of the {\em continuum} classical theory yields a quantum theory which lives on a discrete spacetime lattice. We explicitly construct a state in the polymer Hilbert space which reproduces the standard Fock vacuum- two point functions for long wavelength modes of the scalar field. Our construction indicates that the continuum classical theory emerges under coarse graining. All our considerations are free of the "triangulation" ambiguities which plague attempts to define quantum dynamics in LQG. Our work constitutes the first complete LQG type quantization of a generally covariant field theory together with a semi-classical analysis of the true degrees of freedom and thus provides a perfect infinite dimensional toy model to study open issues in LQG, particularly those pertaining to the definition of quantum dynamics.Comment: 58 page

Implications of Limits of Detection of Various Methods for Bacillus anthracis in Computing Risks to Human Health▿ †

Used for decades for biological warfare, Bacillus anthracis (category A agent) has proven to be highly stable and lethal. Quantitative risk assessment modeling requires descriptive statistics of the limit of detection to assist in defining the exposure. Furthermore, the sensitivities of various detection methods in environmental matrices are vital information for first responders. A literature review of peer-reviewed journal articles related to methods for detection of B. anthracis was undertaken. Articles focused on the development or evaluation of various detection approaches, such as PCR, real-time PCR, immunoassay, etc. Real-time PCR and PCR were the most sensitive methods for the detection of B. anthracis, with median instrument limits of detection of 430 and 440 cells/ml, respectively. There were very few peer-reviewed articles on the detection methods for B. anthracis in the environment. The most sensitive limits of detection for the environmental samples were 0.1 CFU/g for soil using PCR-enzyme-linked immunosorbent assay (ELISA), 17 CFU/liter for air using an ELISA-biochip system, 1 CFU/liter for water using cultivation, and 1 CFU/cm2 for stainless steel fomites using cultivation. An exponential dose-response model for the inhalation of B. anthracis estimates of risk at concentrations equal to the environmental limit of detection determined the probability of death if untreated to be as high as 0.520. Though more data on the environmental limit of detection would improve the assumptions made for the risk assessment, this study's quantification of the risk posed by current limitations in the knowledge of detection methods should be considered when employing those methods in environmental monitoring and cleanup strategies