Models for Modules

We recall the structure of the indecomposable sl(2) modules in the Bernstein-Gelfand-Gelfand category O. We show that all these modules can arise as quantized phase spaces of physical models. In particular, we demonstrate in a path integral discretization how a redefined action of the sl(2) algebra over the complex numbers can glue finite dimensional and infinite dimensional highest weight representations into indecomposable wholes. Furthermore, we discuss how projective cover representations arise in the tensor product of finite dimensional and Verma modules and give explicit tensor product decomposition rules. The tensor product spaces can be realized in terms of product path integrals. Finally, we discuss relations of our results to brane quantization and cohomological calculations in string theory.Comment: 18 pages, 6 figure

Hiding Anomalies

Anomalies can be anticipated at the classical level without changing the classical cohomology, by introducing extra degrees of freedom. In the process, the anomaly does not quite disappear. We show that, in fact, it is shifted to new symmetries that come with the extra fields.Comment: 10

The regularized BRST Jacobian of pure Yang-Mills theory

The Jacobian for infinitesimal BRST transformations of path integrals for pure Yang-Mills theory, viewed as a matrix \unity +\Delta J in the space of Yang-Mills fields and (anti)ghosts, contains off-diagonal terms. Naively, the trace of $\Delta J$ vanishes, being proportional to the trace of the structure constants. However, the consistent regulator \cR, constructed from a general method, also contains off-diagonal terms. An explicit computation demonstrates that the regularized Jacobian Tr\ \Delta J\exp -\cR /M^2 for $M^2\rightarrow \infty$ is the variation of a local counterterm, which we give. This is a direct proof at the level of path integrals that there is no BRST anomaly.Comment: 12 pages, latex, CERN-TH.6541/92, KUL-TF-92/2

Batalin-Vilkovisky gauge-fixing of a chiral two-form in six dimensions

We perform the gauge-fixing of the theory of a chiral two-form boson in six dimensions starting from the action given by Pasti, Sorokin and Tonin. We use the Batalin-Vilkovisky formalism, introducing antifields and writing down an extended action satisfying the classical master equation. Then we gauge-fix the three local symmetries of the extended action in two different ways.Comment: 15 pages, latex, no figures, version accepted by Class. Quant. Gra

Modeling the ecology and evolution of communities: A review of past achievements, current efforts, and future promises

Background: The complexity and dynamical nature of community interactions make modeling a useful tool for understanding how communities develop over time and how they respond to external perturbations. Large community-evolution models (LCEMs) are particularly promising, since they can address both ecological and evolutionary questions, and can give rise to richly structured and diverse model communities. Questions: Which types of models have been used to study community structure and what are their key features and limitations? How do adaptations and/or invasions affect community formation? Which mechanisms promote diverse and table communities? What are the implications of LCEMs for management and conservation? What are the key challenges for future research? Models considered: Static models of community structure, demographic community models, and small and large community- evolution models. Conclusions: LCEMs encompass a variety of modeled traits and interactions, demographic dynamics, and evolutionary dynamics. They are able to reproduce empirical community structures. Already, they have generated new insights, such as the dual role of competition, which limits diversity through competitive exclusion, yet facilitates diversity through speciation. Other critical factors determining eventual community structure are the shape of trade-off functions, inclusion of adaptive foraging, and energy availability. A particularly interesting feature of LCEMs is that these models not only help to contrast outcomes of community formation via species assembly with those of community formation via gradual evolution and speciation, but that they can furthermore unify the underlying invasion processes and evolutionary processes into a single framework

Global Anomalies in the Batalin Vilkovisky Quantization

The Batalin Vilkovisky (BV) quantization provides a general procedure for calculating anomalies associated to gauge symmetries. Recent results show that even higher loop order contributions can be calculated by introducing an appropriate regularization-renormalization scheme. However, in its standard form, the BV quantization is not sensible to quantum violations of the classical conservation of Noether currents, the so called global anomalies. We show here that the BV field antifield method can be extended in such a way that the Ward identities involving divergencies of global Abelian currents can be calculated from the generating functional, a result that would not be obtained by just associating constant ghosts to global symmetries. This extension, consisting of trivially gauging the global Abelian symmetries, poses no extra obstruction to the solution of the master equation, as it happens in the case of gauge anomalies. We illustrate the procedure with the axial model and also calculating the Adler Bell Jackiw anomaly.Comment: We emphasized the fact that our procedure only works for the case of Abelian global anomalies. Section 3 was rewritten and some references were added. 12 pages, LATEX. Revised version that will appear in Phys. Rev.

Thermal radiation in non-static curved spacetimes: quantum mechanical path integrals and configuration space topology

A quantum mechanical path integral derivation is given of a thermal propagator in non-static Gui spacetime. The thermal nature of the propagator is understood in terms of homotopically non-trivial paths in the configuration space appropriate to tortoise coordinates. The connection to thermal emission from collapsing black holes is discussed.Comment: 20 pages, major revised version, 9 figures, new titl

Enhanced production of biologically active interleukin-1α and interleukin-1β by psoriatic epidermal cells ex vivo: Evidence of increased cytosolic interleukin-1β levels and facilitated interleukin-1 release

The expression of interleukin (IL)-1 is altered in psoriatic lesions. However, little is known about the actual production of IL-1α and IL-1β by psoriatic epidermal cells (EC). We monitored IL-1 in the extracellular, the membrane and the intracellular compartment of freshly isolated EC from untreated lesional psoriatic (PP) and normal healthy (NN) skin during non-stimulated short-term cultures, representing a psoriasis model ex vivo. Cytokines were measured using bioassays combined with neutralizing antibodies and enzyme-linked immunosorbent assay in parallel. PP EC released significantly increased amounts of biologically active IL-1α and IL-1β in a ratio of 3:1, whereas NN EC only released IL-1α. Also, the release of IL-6, but not of TNF-α, by PP EC was significantly increased. Membrane-associated IL-1 activity, analyzed using glutaraldehydefixed EC, was low and not unique to PP EC. The cytosol of PP EC contained significantly increased levels of immunoreactive IL-1β. Furthermore, PP EC displayed loss of membrane integrity, as determined by trypan blue exclusion and release of cytosolic lactate dehydrogenase. This facilitated release of intracellular IL-1. Depletion of CD45+ cells showed that intraepidermal leukocytes did not contribute to the production of IL-1. Our observations show that resident PP EC express enhanced IL-1 production ex vivo, which is due to an increased cytosolic IL-1β content and facilitated IL-1 release. This study provides the first evidence that PP EC can produce bioactive IL-1β