896 research outputs found
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
Field Strength Correlators For 2D Yang-Mills Over Riemann Surfaces
The path integral computation of field strength correlation functions for two
dimensional Yang-Mills theories over Riemann surfaces is studied. The
calculation is carried out by abelianization, which leads to correlators that
are topological. They are nontrivial as a result of the topological
obstructions to the abelianization. It is shown in the large N limit on the
sphere that the correlators undergo second order phase transitions at the
critical point. Our results are applied to a computation of contractible Wilson
loops.Comment: final version to appear in Int. Jour. Mod. Phys. A, minor
corrections, added a few comments on Wilson loops and non-abelian Stokes
theore
Human motion analysis and simulation tools: a survey
Computational systems to identify objects represented in image sequences and tracking their motion in a fully automatic manner, enabling a detailed analysis of the involved motion and its simulation are extremely relevant in several fields of our society. In particular, the analysis and simulation of the human motion has a wide spectrum of relevant applications with a manifest social and economic impact. In fact, usage of human motion data is fundamental in a broad number of domains (e.g.: sports, rehabilitation, robotics, surveillance, gesture-based user interfaces, etc.). Consequently, many relevant engineering software applications have been developed with the purpose of analyzing and/or simulating the human motion. This chapter presents a detailed, broad and up to date survey on motion simulation and/or analysis software packages that have been developed either by the scientific community or commercial entities. Moreover, a main contribution of this chapter is an effective framework to classify and compare motion simulation and analysis tools
A Note on the Picard-Fuchs Equations for N=2 Seiberg-Witten Theories
A concise presentation of the PF equations for N=2 Seiberg-Witten theories
for the classical groups of rank r with N_f massless hypermultiplets in the
fundamental representation is provided. For N_f=0, all r PF equations can be
given in a generic form. For certain cases with N_f\neq zero, not all equations
are generic. However, in all cases there are at least r-2 generic PF equations.
For these cases the classical part of the equations is generic, while the
quantum part can be formulated using a method described in a previous paper by
the authors, which is well suited to symbolic computer calculations.Comment: 25 pages, Latex; some new references adde
Coherent state transforms and vector bundles on elliptic curves
AbstractWe extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k, rank n and genus one non-abelian theta functions with the unitarity of the CST transform being preserved. Furthermore, the shift in the level k→k+n appears in a natural way in this finite-dimensional framework
- …