Physical Properties of Quantum Field Theory Measures

Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with different masses is studied. We apply the same methods to study the Ashtekar-Lewandowski (AL) measure on spaces of connections. We prove that the diffeomorphism group acts ergodically, with respect to the AL measure, on the Ashtekar-Isham space of quantum connections modulo gauge transformations. We also prove that a typical, with respect to the AL measure, quantum connection restricted to a (piecewise analytic) curve leads to a parallel transport discontinuous at every point of the curve.Comment: 24 pages, LaTeX, added proof for section 4.2, added reference

Toric K\"ahler metrics seen from infinity, quantization and compact tropical amoebas

We consider the metric space of all toric K\"ahler metrics on a compact toric manifold; when "looking at it from infinity" (following Gromov), we obtain the tangent cone at infinity, which is parametrized by equivalence classes of complete geodesics. In the present paper, we study the associated limit for the family of metrics on the toric variety, its quantization, and degeneration of generic divisors. The limits of the corresponding K\"ahler polarizations become degenerate along the Lagrangian fibration defined by the moment map. This allows us to interpolate continuously between geometric quantizations in the holomorphic and real polarizations and show that the monomial holomorphic sections of the prequantum bundle converge to Dirac delta distributions supported on Bohr-Sommerfeld fibers. In the second part, we use these families of toric metric degenerations to study the limit of compact hypersurface amoebas and show that in Legendre transformed variables they are described by tropical amoebas. We believe that our approach gives a different, complementary, perspective on the relation between complex algebraic geometry and tropical geometry.Comment: v1: 32 pages, 5 figures; v2: 1 figure added; v3: 1 reference added; v4: some reorganization, 1 theorem (now 1.1) added; v5: final version, to appear in JD

Utilização econômica da fauna silvestre no Brasil: o exemplo do Jacaré-do-Pantanal.

bitstream/CPAP/56461/1/ADM005.pdfFormato eletrônico

Corredores ecológicos e ecoturismo no Pantanal.

bitstream/CPAP/56451/1/ADM014.pdfFormato eletrônico