Proof of Divergence of the Perturbative Series for a Large Collection of Scalar Field Models in Euclidean Lattice Quantum Field Theory
Abstract
We present a simple but rigorous mathematical proof, based on well-knowntheorems about power series in the theory of analytic functions, thatthe perturbative series of a large number of scalar field models inlattice quantum field theory, with interaction terms that are given by$\lambda\varphi^{2p}$ for $p\geq 2$, are divergent at all points excepttheir points of reference $\lambda=0$. This is true not only in thecontinuum limit, but on every individual finite lattice as well, for allspacetime dimensions $d\geq 3$.
Fields of Study & Subjects
Theoretical and Computational Physics
advanced mathematical theories
Quantum Chromodynamics and Particle Interactions
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 17 February 2026
- Language
- EN
- Document type
- Preprint