Krull-tropical hypersurfaces

The concepts of tropical-semiring and tropical hypersurface, are extended for an arbitrary ordered group. Then, we define the tropicalization of a polynomial with coefficients in a Krull-valued field. After a close study of the properties of the operator "tropicalization" we conclude with an extension of Kapranov's theorem to algebraically closed fields together with a valuation over an ordered group.Comment: 12 page

Matter Fields in the Lagrangian Loop Representation: Scalar QED

We present the extension of the Lagrangian loop gauge invariant representation in such a way to include matter fields. The partition function of lattice compact U(1)-Higgs model is expressed as a sum over closed as much as open surfaces. We have simulated numerically the loop action equivalent to the Villain form of the action and mapped out the beta-gamma phase diagram of this model.Comment: 10 pages, LaTe

Support of Laurent series algebraic over the field of formal power series

This work is devoted to the study of the support of a Laurent series in several variables which is algebraic over the ring of power series over a characteristic zero field. Our first result is the existence of a kind of maximal dual cone of the support of such a Laurent series. As an application of this result we provide a gap theorem for Laurent series which are algebraic over the field of formal power series. We also relate these results to diophantine properties of the fields of Laurent series.Comment: 31 pages. To appear in Proc. London Math. So

The Worldsheet Formulation as an Alternative Method for Simulating Dynamical Fermions

The recently proposed worldsheet formulation of lattice fermions is tested for the first time carrying out a simulation for the simplest model: the one-flavor, strictly massless lattice Schwinger model. A main advantage of this alternative method for simulating dynamical fermions consists in its economy: it involves many fewer degrees of freedom than the ordinary Kogut-Susskind formulation. The known continuum limit is reproduced by the method for relatively small lattices.Comment: 4 pages, 1 eps figure, revte

Numerical Computations in the Worldsheet Formulation

The worldsheet formulation of lattice gauge theories has two appealing features: the gauge non-redundancy and the geometrical transparency. Both properties are profitable in order to perform numerical computations. In the case of dynamical fermions this description offers additional advantages. For instance, it does not suffer from the species doubling problem and it involves fewer degrees of freedom.Comment: Talk presented at LATTICE 97, Edinburgh. 3 pages, 2 .eps figures, uses espcrc2.st