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Triviality proof for mean-field $\varphi_4^4$-theories
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abstract
The differential equations of the Wilson renormalization group are a powerful tool to study the Schwinger functions of Euclidean quantum field theory. In particular renormalization theory can be based entirely on inductively bounding their perturbatively expanded solutions. Recently the solutions of these equations for scalar field theory have been analysed rigorously without recourse to perturbation theory, at the cost of restricting to the mean-field approximation. In particular it was shown there that one-component $\varphi^4_4$-theory is trivial if the bare coupling constant of the UV regularized theory is not large. This paper presents progress w.r.t. Kopper's previous paper on asymptotically free solutions of the mean-field scalar flow equations: 1. The upper bound on the bare coupling is sent to infinity and the proof is extended to $O(N)$ vector models. 2. The unphysical infrared cutoff used for technical simplicity is replaced by a physical mass.
Forward citations
Cited by 2 Pith papers
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Exact Schwinger functions for a class of bounded interactions in $d\geq 2$
Exact UV limits of connected Schwinger functions (n≠2) for bounded interactions in d≥2 equal tree-level 1PI functions of the erf(φ/√2) theory.
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Triviality in a Non-Perturbative Second-Order Mean-Field Theory for $\phi^4_4$
A second-order mean-field truncation of the phi^4_4 Wilson-Polchinski hierarchy is shown to have smooth solutions that converge to the Gaussian fixed point for any positive bare coupling.
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