103,360 research outputs found
New Numerical Method for Fermion Field Theory
A new deterministic, numerical method to solve fermion field theories is
presented. This approach is based on finding solutions to the lattice
functional equations for field theories in the presence of an external source
. Using Grassmann polynomial expansions for the generating functional ,
we calculate propagators for systems of interacting fermions. These
calculations are straightforward to perform and are executed rapidly compared
to Monte Carlo. The bulk of the computation involves a single matrix inversion.
Because it is not based on a statistical technique, it does not have many of
the difficulties often encountered when simulating fermions. Since no
determinant is ever calculated, solutions to problems with dynamical fermions
are handled more easily. This approach is very flexible, and can be taylored to
specific problems based on convenience and computational constraints. We
present simple examples to illustrate the method; more general schemes are
desirable for more complicated systems.Comment: 24 pages, latex, figures separat
Construction of Special Solutions for Nonintegrable Systems
The Painleve test is very useful to construct not only the Laurent series
solutions of systems of nonlinear ordinary differential equations but also the
elliptic and trigonometric ones. The standard methods for constructing the
elliptic solutions consist of two independent steps: transformation of a
nonlinear polynomial differential equation into a nonlinear algebraic system
and a search for solutions of the obtained system. It has been demonstrated by
the example of the generalized Henon-Heiles system that the use of the Laurent
series solutions of the initial differential equation assists to solve the
obtained algebraic system. This procedure has been automatized and generalized
on some type of multivalued solutions. To find solutions of the initial
differential equation in the form of the Laurent or Puiseux series we use the
Painleve test. This test can also assist to solve the inverse problem: to find
the form of a polynomial potential, which corresponds to the required type of
solutions. We consider the five-dimensional gravitational model with a scalar
field to demonstrate this.Comment: LaTeX, 14 pages, the paper has been published in the Journal of
Nonlinear Mathematical Physics (http://www.sm.luth.se/math/JNMP/
Computation with Polynomial Equations and Inequalities arising in Combinatorial Optimization
The purpose of this note is to survey a methodology to solve systems of
polynomial equations and inequalities. The techniques we discuss use the
algebra of multivariate polynomials with coefficients over a field to create
large-scale linear algebra or semidefinite programming relaxations of many
kinds of feasibility or optimization questions. We are particularly interested
in problems arising in combinatorial optimization.Comment: 28 pages, survey pape
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