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February 19, 20260 citationsOpen Access

Proof of Divergence of the Perturbative Series for a Large Collection of Scalar Field Models in Euclidean Lattice Quantum Field Theory

JDJorge L. deLyra

Key Points

  • To rigorously prove the divergence of perturbative series in scalar field models on lattice quantum field theory.
  • Mathematical proof utilizing theorems of power series in analytic functions.
  • Analysis of interaction terms given by λφ²ᵖ for p≥2.
  • Examination of results across different lattice structures and spacetime dimensions.
  • Perturbative series are divergent at all points except λ=0.
  • This divergence holds in the continuum limit and on finite lattices.
  • Applicable to all spacetime dimensions d≥3.

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^2p for p 2, are divergent at all points excepttheir points of reference =0. This is true not only in thecontinuum limit, but on every individual finite lattice as well, for allspacetime dimensions d 3.

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Cite This Study

Jorge L. deLyra (2026) studied this question.

synapsesocial.com/papers/6996a8e3ecb39a600b3f00dfhttps://doi.org/10.5281/zenodo.18670820
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