2,023 research outputs found
Metrics on semistable and numerically effective Higgs bundles
We provide notions of numerical effectiveness and numerical flatness for
Higgs vector bundles on compact K\"ahler manifolds in terms of fibre metrics.
We prove several properties of bundles satisfying such conditions and in
particular we show that numerically flat Higgs bundles have vanishing Chern
classes, and that they admit filtrations whose quotients are stable flat Higgs
bundles. We compare these definitions with those previously given in the case
of projective varieties. Finally we study the relations between numerically
effectiveness and semistability, establishing semistability criteria for Higgs
bundles on projective manifolds of any dimension.Comment: 25 pages. Changes in the expositio
Boundary Exchange Algebras and Scattering on the Half Line
Some algebraic aspects of field quantization in space-time with boundaries
are discussed. We introduce an associative algebra, whose exchange properties
are inferred from the scattering processes in integrable models with reflecting
boundary conditions on the half line. The basic properties of this algebra are
established and the Fock representations associated with certain involutions
are derived. We apply these results for the construction of quantum fields and
for the study of scattering on the half line.Comment: Enlarged version, to appear in Comm. Math. Phys. Tex file, macros
included, no figures, 32 page
- …