Gerbes and Heisenberg's Uncertainty Principle

We prove that a gerbe with a connection can be defined on classical phase space, taking the U(1)-valued phase of certain Feynman path integrals as Cech 2-cocycles. A quantisation condition on the corresponding 3-form field strength is proved to be equivalent to Heisenberg's uncertainty principle.Comment: 12 pages, 1 figure available upon reques

Path-Integral for Quantum Tunneling

Path-integral for theories with degenerate vacua is investigated. The origin of the non Borel-summability of the perturbation theory is studied. A new prescription to deal with small coupling is proposed. It leads to a series, which at low orders and small coupling differs from the ordinary perturbative series by nonperturbative amount, but is Borel-summable.Comment: 25 pages + 12 figures (not included, but available upon request) [No changed in content in this version. Problem with line length fixed.

The transition temperature of the dilute interacting Bose gas for NN internal degrees of freedom

We calculate explicitly the variation $\delta T_c$ of the Bose-Einstein condensation temperature $T_c$ induced by weak repulsive two-body interactions to leading order in the interaction strength. As shown earlier by general arguments, $\delta T_c/T_c$ is linear in the dimensionless product $an^{1/3}$ to leading order, where $n$ is the density and $a$ the scattering length. This result is non-perturbative, and a direct perturbative calculation of the amplitude is impossible due to infrared divergences familiar from the study of the superfluid helium lambda transition. Therefore we introduce here another standard expansion scheme, generalizing the initial model which depends on one complex field to one depending on $N$ real fields, and calculating the temperature shift at leading order for large $N$. The result is explicit and finite. The reliability of the result depends on the relevance of the large $N$ expansion to the situation N=2, which can in principle be checked by systematic higher order calculations. The large $N$ result agrees remarkably well with recent numerical simulations.Comment: 10 pages, Revtex, submitted to Europhysics Letter

Refined Cauchy/Littlewood identities and six-vertex model partition functions: II. Proofs and new conjectures

We prove two identities of Hall-Littlewood polynomials, which appeared recently in a paper by two of the authors. We also conjecture, and in some cases prove, new identities which relate infinite sums of symmetric polynomials and partition functions associated with symmetry classes of alternating sign matrices. These identities generalize those already found in our earlier paper, via the introduction of additional parameters. The left hand side of each of our identities is a simple refinement of a relevant Cauchy or Littlewood identity. The right hand side of each identity is (one of the two factors present in) the partition function of the six-vertex model on a relevant domain.Comment: 34 pages, 14 figure

A Weyl-covariant tensor calculus

On a (pseudo-) Riemannian manifold of dimension n > 2, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives the conformally invariant Weyl tensor plus the Cotton tensor. So-called generalized connections and their transformation laws under diffeomorphisms and Weyl rescalings are also derived. These results are obtained by application of BRST techniques.Comment: LaTeX, 10 pages. Minor corrections and a reference adde

The prediction of nonlinear longitudinal combustion instability in liquid propellant rockets

An analytical technique was developed to solve nonlinear longitudinal combustion instability problems. The analysis yields the transient and limit cycle behavior of unstable motors and the threshold amplitude required to trigger a linearly stable motor into unstable operation. The limit cycle waveforms were found to exhibit shock wave characteristics for most unstable engine operating conditions. A method of correlating the analytical solutions with experimental data was developed. Calculated results indicate that a second-order solution adequately describes the behavior of combustion instability oscillations over a broad range of engine operating conditions, but that higher order effects must be accounted for in order to investigate engine triggering

Discrete holomorphicity and quantized affine algebras

We consider non-local currents in the context of quantized affine algebras, following the construction introduced by Bernard and Felder. In the case of $U_q(A_1^{(1)})$ and $U_q(A_2^{(2)})$, these currents can be identified with configurations in the six-vertex and Izergin--Korepin nineteen-vertex models. Mapping these to their corresponding Temperley--Lieb loop models, we directly identify non-local currents with discretely holomorphic loop observables. In particular, we show that the bulk discrete holomorphicity relation and its recently derived boundary analogue are equivalent to conservation laws for non-local currents

The two-point correlation function of three-dimensional O(N) models: critical limit and anisotropy

In three-dimensional O(N) models, we investigate the low-momentum behavior of the two-point Green's function G(x) in the critical region of the symmetric phase. We consider physical systems whose criticality is characterized by a rotational-invariant fixed point. Several approaches are exploited, such as strong-coupling expansion of lattice non-linear O(N) sigma models, 1/N-expansion, field-theoretical methods within the phi^4 continuum formulation. In non-rotational invariant physical systems with O(N)-invariant interactions, the vanishing of space-anisotropy approaching the rotational-invariant fixed point is described by a critical exponent rho, which is universal and is related to the leading irrelevant operator breaking rotational invariance. At N=\infty one finds rho=2. We show that, for all values of $N\geq 0$, $\rho\simeq 2$. Non-Gaussian corrections to the universal low-momentum behavior of G(x) are evaluated, and found to be very small.Comment: 65 pages, revte

A study of crop income fluctuations for farm plans developed to meet specified soil erosion loss levels on four West Tennessee farms

Four West Tennessee upland row crop farms were selected as representative of those in the area. Soil losses were estimated for the farmers\u27 current soil management system using the Universal Soil Loss Predicting Equation. The returns to land and management generated by the farmers\u27 current soil management system were estimated using yield data and crop budgets published in University of Tennessee Agricultural Experiment Station Bulletins. A set of fifteen cropping systems and four soil management practices were used to develop soil management plans to hold soil losses at approximately 5 ton/acre/year, 10 ton/acre/year and greater than or equal to 20 ton/acre/year. One set of plans included the use of minimum tillage, the other did not. The results showed it was possible on three of the farms to hold estimated soil losses at approximately 5 ton/acre/year and increase estimated returns to land and management over the returns estimated for the farmer\u27s current soil management system. On the remaining farm, estimated returns to land and management for the farmer\u27s present soil management system were only slightly higher than those estimated for the 5 ton/acre/year plan with minimum tillage

The Application of Mass Spectrometric Measurement Techniques for the Evaluation and Assessment of Autism Spectrum Disorders

Autism spectrum disorders (ASDs) are neurological developmental disorders that affect communication and social interaction. They are becoming more important to society as their rate has risen dramatically over the past 30 years. Presently, there is no known cure for ASDs and the current research focuses on improvements in diagnosis and different types of treatments. The most significant contribution of the research described in this dissertation is the application of advanced mass spectrometric measurement techniques that provide higher accuracy and precision to the diagnosis and treatment of ASDs. The treatment of ASDs was assessed through the evaluation of elemental contamination in dietary supplements. Elemental contamination was discovered to exist in the dietary supplements through the application of standard United States Environmental Protection Agency methods for both sample preparation and analysis. The diagnosis of ASDs was evaluated through the search for biomarkers. The plasma zinc/serum copper ratio may be a biomarker that indicates stress on the metallothionein system of children with ASDs. Biomarkers during treatment in autism were sought in a cleanroom study demonstrating that the younger children responded better to the cleanroom experience compared to older children through noteworthy behavioral and physiological changes. The comparative analysis of children with autism and controls had results indicating the possibility of children with autism showing characteristics of the toxicant-induced loss of tolerance theory of disease. Measurement comparisons were performed between the analytical methods and the commercial clinical laboratory that demonstrated the superior quality of the analytical measurements. Overall, the work described in this dissertation demonstrated the power of advanced mass spectrometric analysis techniques through the application to the diagnosis and treatment of ASDs. A greater understanding of children with autism has been accomplished through the discovery of potential biomarkers and characteristics unique to them. The work in this dissertation can be applied to other diseases and other types of measurements using the principles described throughout it. Finally, the work has shown the importance of measurement in achieving accurate and precise data that leads to the greatest understanding and knowledge