7,653 research outputs found
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
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