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O(N)-symmetric (lambda)(phi)4 theory: the gaussin effective potential approach

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The O(N)-symmetric generalization of λ φ 4 theory is studied in the Gaussian-effective-potential (GEP) approach. It is shown that the GEP encompasses and transcends the leading-order 1/N expansion results. We find two distinct, nontrivial versions of the (3+1)-dimensional theory: (i) ‘‘precarious φ 4 theory,’’ with negative, infinitesimal λ B , which coincides with the 1/N result; and (ii) ‘‘autonomous φ 4 theory,’’ with positive, infinitesimal λ B and an infinite wave-function renormalization, which is inaccessible to perturbative or 1/N methods, and could well have eluded lattice-based approaches. ‘‘Autonomous φ 4 theory’’ can exhibit spontaneous symmetry breaking, and we speculate on its relevance for the Higgs mechanism.

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STEVENSON, P. m., ALLÉS, B., TARRACH, R.. O(N)-symmetric (lambda)(phi)4 theory: the gaussin effective potential approach. _Physical Review D_. 1987. Vol. 35, núm. 8, pàgs. 2407-2414. [consulta: 11 de abril de 2026]. ISSN: 0556-2821. [Disponible a: https://hdl.handle.net/2445/12423]

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