Entwined Paths, Difference Equations and the Dirac Equation

Entwined space-time paths are bound pairs of trajectories which are traversed in opposite directions with respect to macroscopic time. In this paper we show that ensembles of entwined paths on a discrete space-time lattice are simply described by coupled difference equations which are discrete versions of the Dirac equation. There is no analytic continuation, explicit or forced, involved in this description. The entwined paths are `self-quantizing'. We also show that simple classical stochastic processes that generate the difference equations as ensemble averages are stable numerically and converge at a rate governed by the details of the stochastic process. This result establishes the Dirac equation in one dimension as a phenomenological equation describing an underlying classical stochastic process in the same sense that the Diffusion and Telegraph equations are phenomenological descriptions of stochastic processes.Comment: 15 pages, 5 figures Replacement 11/02 contains minor editorial change

Superinflation, quintessence, and nonsingular cosmologies

The dynamics of a universe dominated by a self-interacting nonminimally coupled scalar field are considered. The structure of the phase space and complete phase portraits are given. New dynamical behaviors include superinflation ($\dot{H}>0$), avoidance of big bang singularities through classical birth of the universe, and spontaneous entry into and exit from inflation. This model is promising for describing quintessence as a nonminimally coupled scalar field.Comment: 4 pages, 2 figure

Renormalization-Group Improved Effective Potential for Interacting Theories with Several Mass Scales in Curved Spacetime

The renormalization group (RG) is used in order to obtain the RG improved effective potential in curved spacetime. This potential is explicitly calculated for the Yukawa model and for scalar electrodynamics, i.e. theories with several (namely, more than one) mass scales, in a space of constant curvature. Using the $\lambda \varphi^4$-theory on a general curved spacetime as an example, we show how it is possible to find the RG improved effective Lagrangian in curved spacetime. As specific applications, we discuss the possibility of curvature induced phase transitions in the Yukawa model and the effective equations (back-reaction problem) for the $\lambda \varphi^4$-theory on a De Sitter background.Comment: 18 pages, LaTeX file, UB-ECM-PF 93/2

Glassy Vortex State in a Two-Dimensional Disordered XY-Model

The two-dimensional XY-model with random phase-shifts on bonds is studied. The analysis is based on a renormalization group for the replicated system. The model is shown to have an ordered phase with quasi long-range order. This ordered phase consists of a glass-like region at lower temperatures and of a non-glassy region at higher temperatures. The transition from the disordered phase into the ordered phase is not reentrant and is of a new universality class at zero temperature. In contrast to previous approaches the disorder strength is found to be renormalized to larger values. Several correlation functions are calculated for the ordered phase. They allow to identify not only the transition into the glassy phase but also an additional crossover line, where the disconnected vortex correlation changes its behavior on large scales non-analytically. The renormalization group approach yields the glassy features without a breaking of replica symmetry.Comment: latex 12 pages with 3 figures, using epsf.sty and multicol.st

Farming and the geography of nutrient production for human use: a transdisciplinary analysis

Background: Information about the global structure of agriculture and nutrient production and its diversity is essential to improve present understanding of national food production patterns, agricultural livelihoods, and food chains, and their linkages to land use and their associated ecosystems services. Here we provide a plausible breakdown of global agricultural and nutrient production by farm size, and also study the associations between farm size, agricultural diversity, and nutrient production. This analysis is crucial to design interventions that might be appropriately targeted to promote healthy diets and ecosystems in the face of population growth, urbanisation, and climate change. Methods: We used existing spatially-explicit global datasets to estimate the production levels of 41 major crops, seven livestock, and 14 aquaculture and fish products. From overall production estimates, we estimated the production of vitamin A, vitamin B₁₂, folate, iron, zinc, calcium, calories, and protein. We also estimated the relative contribution of farms of different sizes to the production of different agricultural commodities and associated nutrients, as well as how the diversity of food production based on the number of different products grown per geographic pixel and distribution of products within this pixel (Shannon diversity index [H]) changes with different farm sizes. Findings: Globally, small and medium farms (≤50 ha) produce 51–77% of nearly all commodities and nutrients examined here. However, important regional differences exist. Large farms (>50 ha) dominate production in North America, South America, and Australia and New Zealand. In these regions, large farms contribute between 75% and 100% of all cereal, livestock, and fruit production, and the pattern is similar for other commodity groups. By contrast, small farms (≤20 ha) produce more than 75% of most food commodities in sub-Saharan Africa, southeast Asia, south Asia, and China. In Europe, west Asia and north Africa, and central America, medium-size farms (20–50 ha) also contribute substantially to the production of most food commodities. Very small farms (≤2 ha) are important and have local significance in sub-Saharan Africa, southeast Asia, and south Asia, where they contribute to about 30% of most food commodities. The majority of vegetables (81%), roots and tubers (72%), pulses (67%), fruits (66%), fish and livestock products (60%), and cereals (56%) are produced in diverse landscapes (H>1·5). Similarly, the majority of global micronutrients (53–81%) and protein (57%) are also produced in more diverse agricultural landscapes (H>1·5). By contrast, the majority of sugar (73%) and oil crops (57%) are produced in less diverse ones (H≤1·5), which also account for the majority of global calorie production (56%). The diversity of agricultural and nutrient production diminishes as farm size increases. However, areas of the world with higher agricultural diversity produce more nutrients, irrespective of farm size. Interpretation: Our results show that farm size and diversity of agricultural production vary substantially across regions and are key structural determinants of food and nutrient production that need to be considered in plans to meet social, economic, and environmental targets. At the global level, both small and large farms have key roles in food and nutrition security. Efforts to maintain production diversity as farm sizes increase seem to be necessary to maintain the production of diverse nutrients and viable, multifunctional, sustainable landscapes. Funding: Commonwealth Scientific and Industrial Research Organisation, Bill & Melinda Gates Foundation, CGIAR Research Programs on Climate Change, Agriculture and Food Security and on Agriculture for Nutrition and Health funded by the CGIAR Fund Council, Daniel and Nina Carasso Foundation, European Union, International Fund for Agricultural Development, Australian Research Council, National Science Foundation, Gordon and Betty Moore Foundation, and Joint Programming Initiative on Agriculture, Food Security and Climate Change—Belmont Forum

A-dependence of nuclear transparency in quasielastic A(e,e'p) at high Q^2

The A-dependence of the quasielastic A(e,e'p) reaction has been studied at SLAC with H-2, C, Fe, and Au nuclei at momentum transfers Q^2 = 1, 3, 5, and 6.8 (GeV/c)^2. We extract the nuclear transparency T(A,Q^2), a measure of the average probability that the struck proton escapes from the nucleus A without interaction. Several calculations predict a significant increase in T with momentum transfer, a phenomenon known as Color Transparency. No significant rise within errors is seen for any of the nuclei studied.Comment: 5 pages incl. 2 figures, Caltech preprint OAP-73

Quantum mechanics: Myths and facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.Comment: 51 pages, pedagogic review, revised, new references, to appear in Found. Phy

Coupled oscillators as models of phantom and scalar field cosmologies

We study a toy model for phantom cosmology recently introduced in the literature and consisting of two oscillators, one of which carries negative kinetic energy. The results are compared with the exact phase space picture obtained for similar dynamical systems describing, respectively, a massive canonical scalar field conformally coupled to the spacetime curvature, and a conformally coupled massive phantom. Finally, the dynamical system describing exactly a minimally coupled phantom is studied and compared with the toy model.Comment: 18 pages, LaTeX, to appear in Physical Review

Observation of exclusive DVCS in polarized electron beam asymmetry measurements

We report the first results of the beam spin asymmetry measured in the reaction e + p -> e + p + gamma at a beam energy of 4.25 GeV. A large asymmetry with a sin(phi) modulation is observed, as predicted for the interference term of Deeply Virtual Compton Scattering and the Bethe-Heitler process. The amplitude of this modulation is alpha = 0.202 +/- 0.028. In leading-order and leading-twist pQCD, the alpha is directly proportional to the imaginary part of the DVCS amplitude.Comment: 6 pages, 5 figure