Non-perturbative computation of lattice correlation functions by differential equations
arXiv:2210.16052 · doi:10.1103/PhysRevD.107.014502
Abstract
We show that methods developed in the context of perturbative calculations can be transferred to non-perturbative calculations. We demonstrate that correlation functions on the lattice can be computed with the method of differential equations, supplemented with techniques from twisted cohomology. We derive differential equations for the variation with the coupling or -- more generally -- with the parameters of the action. Already simple examples show that the differential equation with respect to the coupling has an essential singularity at zero coupling and a regular singularity at infinite coupling. The properties of the differential equation at zero coupling can be used to prove that the perturbative series is only an asymptotic series.
arXiv comment6 pages, v2: version to be published
References in corpus (19)
- Differential Equations for Two-Loop Four-Point Functions
- Differential Equations for Feynman Graph Amplitudes
- Feynman Integrals and Intersection Theory
- Vector Space of Feynman Integrals and Multivariate Intersection Numbers
- Scattering Amplitudes from Intersection Theory
- Combinatorics and Topology of Kawai-Lewellen-Tye Relations
- Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
- Decomposition of Feynman Integrals by Multivariate Intersection Numbers
- Duals of Feynman Integrals, I: Differential Equations
- From Infinity to Four Dimensions: Higher Residue Pairings and Feynman Integrals
- Duals of Feynman Integrals, 2: Generalized Unitarity
- On the computation of intersection numbers for twisted cocycles
- Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers
- Divergent Perturbation Series
- Status of Intersection Theory and Feynman Integrals
- Twisted de Rham cohomology, homological definition of the integral and "Physics over a ring"
- Correlation functions on the lattice and twisted cocycles
- Batalin-Vilkovisky Integrals in Finite Dimensions
- Homological perturbation theory for nonperturbative integrals