BRST Formulation of Partition Function Constraints

We show that constraints on the generating functional have direct BRST-extensions in terms of nilpotent operators $\Delta$ that annihilate this generating functional, and which may be of arbitrarily high order. The free energy $F$ in the presence of external sources thus satisfies a ``Master Equation'' which is described in terms of a tower of higher antibrackets.Comment: LaTeX, 7 page

Putting an Edge to the Poisson Bracket

We consider a general formalism for treating a Hamiltonian (canonical) field theory with a spatial boundary. In this formalism essentially all functionals are differentiable from the very beginning and hence no improvement terms are needed. We introduce a new Poisson bracket which differs from the usual ``bulk'' Poisson bracket with a boundary term and show that the Jacobi identity is satisfied. The result is geometrized on an abstract world volume manifold. The method is suitable for studying systems with a spatial edge like the ones often considered in Chern-Simons theory and General Relativity. Finally, we discuss how the boundary terms may be related to the time ordering when quantizing.Comment: 36 pages, LaTeX. v2: A manifest formulation of the Poisson bracket and some examples are added, corrected a claim in Appendix C, added an Appendix F and a reference. v3: Some comments and references adde

A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry

We introduce an antisymplectic Dirac operator and antisymplectic gamma matrices. We explore similarities between, on one hand, the Schroedinger-Lichnerowicz formula for spinor bundles in Riemannian spin geometry, which contains a zeroth-order term proportional to the Levi-Civita scalar curvature, and, on the other hand, the nilpotent, Grassmann-odd, second-order \Delta operator in antisymplectic geometry, which in general has a zeroth-order term proportional to the odd scalar curvature of an arbitrary antisymplectic and torsionfree connection that is compatible with the measure density. Finally, we discuss the close relationship with the two-loop scalar curvature term in the quantum Hamiltonian for a particle in a curved Riemannian space.Comment: 55 pages, LaTeX. v2: Subsection 3.10 expanded. v3: Reference added. v4: Published versio

Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent \Delta operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra, and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie brackets with a fixed nilpotent Lie algebra element Q. We find the most general Jacobi-like identity that such a hierarchy satisfies. The numerical coefficients in front of each term in these generalized Jacobi identities are related to the Bernoulli numbers. We suggest that the definition of a homotopy Lie algebra should be enlarged to accommodate this important case. Finally, we consider the Courant bracket as an example of a derived bracket. We extend it to the "big bracket" of exterior forms and multi-vectors, and give closed formulas for the higher Courant brackets.Comment: 42 pages, LaTeX. v2: Added remarks in Section 5. v3: Added further explanation. v4: Minor adjustments. v5: Section 5 completely rewritten to include covariant construction. v6: Minor adjustments. v7: Added references and explanation to Section

Strategies to Stay Alive: Adaptive Toolboxes for Living Well with Suicidal Behavior

Suicidal behavior constitutes a major global problem. Qualitative research utilizing the first-hand experiences of those who have survived attempts to take their own lives can offer much in the way of understanding how to live well despite ongoing suicidal behavior. Given that suicidal intentions and behaviors occur within the person’s subjective construal, the solutions to living—and preferably living well—despite such inclinations must also be subjective and adaptive. The aim of this study was therefore to understand how individuals live with different aspects of their suicidal behavior and their use of effective strategies to protect themselves from future attempts. Thematic analysis of semi-structured, qualitative interviews with 17 participants with lived experience of suicidal behavior from the USA yielded two main themes: (i) the ‘dynamic relationship with suicidal behavior: living with, and through’, and (ii) ‘the toolbox’. Each of these themes had four subthemes. Participants in this study offered important insights into what helped them not just survive ongoing suicidal behavior, but how they created unique toolboxes to continue living, and to live well. These toolboxes contained personalized solutions to dealing with recurring threats to their subjective wellbeing and included diverse solutions from spirituality, pets, peer-support, participating in the arts, through to traditional therapeutic supports. Some participants also discussed the importance of broader social policy and societal changes that help them live. The findings highlight crucial implications for suicide prevention efforts, especially in terms of encouraging collaborations with the lived experience community and furthering a strengths-based approach to mitigating suicidal behaviors. We encourage the clinical community to work in partnership with service-users to enable them to generate effective solutions to living—and living well—through suicidal behavior

Avaliação da vulnerabilidade ambiental das terras da microbacia do córrego Fonseca, região Serrana do estado do Rio de Janeiro.

O objetivo deste trabalho foi avaliar a vulnerabilidade ambiental das terras na área da microbacia do córrego Fonseca, visando fornecer subsídios para o planejamento de uso das terras em pequenas propriedades rurais. Os procedimentos utilizados envolveram a aquisição, conversão e armazenamento de dados básicos em meio digital, construção de um banco de dados digitais, superposição de mapas temáticos em SIG, com atribuição de valores específicos a cada um deles, segundo a importância dos fatores em relação à vulnerabilidade ambiental. O mapa final, produzido na escala 1:10.000, estratifica a área de estudo em 6 classes de vulnerabilidade ambiental, sendo elas: baixa, moderada, alta, alta a muito alta, muito alta e extremamente alta. Os resultados produzidos contribuem para o planejamento ambiental da área

Suscetibilidade dos solos à erosão na microbacia do córrego Fonseca, região Serrana do estado do Rio de Janeiro.

O objetivo deste trabalho foi avaliar a suscetibilidade dos solos à erosão na área da microbacia do córrego Fonseca, visando fornecer subsídios para o planejamento de uso das terras em pequenas propriedades rurais. Os procedimentos utilizados constaram da interpretação de parâmetros dos tipos de solo, cobertura vegetal, litologia, relevo, precipitação e uso das terras, aliados à superposição temática em SIG, com atribuição de valores específicos a cada um deles, segundo o grau de importância desses fatores em relação à erosão. Foi gerado um mapa na escala 1:10.000, estratificado em 7 classes de suscetibilidade à erosão, discriminando e quantificando as classes de erosão que ocorrem na área. Os resultados contribuem para o plano de manejo conservacionista da área de estudo