Real time lattice correlation functions from differential equations

Abstract

Abstract We report on an exact calculation of lattice correlation functions on a finite four-dimensional lattice with either Euclidean or Minkowskian signature. The lattice correlation functions are calculated by the method of differential equations. This method can be used for Euclidean and Minkowskian signature alike. The lattice correlation functions have a power series expansion in 1/ λ $$ \sqrt{\lambda } $$ , where λ is the coupling. We show that this series is convergent for all non-zero values of λ. At small coupling we quantify the accuracy of perturbative approximations. At the technical level we systematically investigate the interplay between twisted cohomology and the symmetries of the twist function.

Keywords

• Algorithms and Theoretical Developments
• Correlation Functions
• Differential and Algebraic Geometry
• Lattice Quantum Field Theory