New Numerical Method for Fermion Field Theory

Abstract

A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using Grassmann polynomial expansions for the generating functional $Z$, 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.

24 pages, latex, figures separate

References in corpus (2)

• A New Approach to Numerical Quantum Field Theory
• Source Galerkin Calculations in Scalar Field Theory

Cited by in corpus (8)

• The Numerical Approximation of Nonlinear Functionals and Functional Differential Equations
• Source Galerkin Calculations in Scalar Field Theory
• A Grassmann integral equation
• New Numerical Methods for Quantum Field Theories on the Continuum
• A Review Of Two Novel Numerical Methods in QFT
• Galerkin Formulation of Path Integrals in Lattice Field Theory
• New Numerical Methods for Iterative or Perturbative Solution of Quantum Field Theory
• Numerical Quantum Field Theory on the Continuum and a New Look at Perturbation Theory