A new proof of the existence and nontriviality of the continuum ϕ24 and ϕ34 quantum field theories

David C. Brydges; Jürg Fröhlich; Alan D. Sokal

doi:10.1007/BF01211157

A new proof of the existence and nontriviality of the continuum ϕ24 and ϕ34 quantum field theories

David C. Brydges, Jürg Fröhlich, Alan D. Sokal

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Abstract

We use Schwinger-Dyson equations combined with rigorous "perturbation-theoretic" correlation inequalities to give a new and extremely simple proof of the existence and nontriviality of the weakly-coupled continuum φ{symbol}₂⁴ and φ{symbol}₃⁴ quantum field theories, constructed as subsequence limits of lattice theories. We prove an asymptotic expansion to order λ or λ² for the correlation functions and for the mass gap. All Osterwalder-Schrader axioms are satisfied except perhaps Euclidean (rotation) invariance.

Original language	English (US)
Pages (from-to)	141-186
Number of pages	46
Journal	Communications In Mathematical Physics
Volume	91
Issue number	2
DOIs	https://doi.org/10.1007/BF01211157
State	Published - Jun 1983

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "We use Schwinger-Dyson equations combined with rigorous {"}perturbation-theoretic{"} correlation inequalities to give a new and extremely simple proof of the existence and nontriviality of the weakly-coupled continuum φ{symbol}24 and φ{symbol}34 quantum field theories, constructed as subsequence limits of lattice theories. We prove an asymptotic expansion to order λ or λ2 for the correlation functions and for the mass gap. All Osterwalder-Schrader axioms are satisfied except perhaps Euclidean (rotation) invariance.",

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year = "1983",

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AU - Sokal, Alan D.

PY - 1983/6

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N2 - We use Schwinger-Dyson equations combined with rigorous "perturbation-theoretic" correlation inequalities to give a new and extremely simple proof of the existence and nontriviality of the weakly-coupled continuum φ{symbol}24 and φ{symbol}34 quantum field theories, constructed as subsequence limits of lattice theories. We prove an asymptotic expansion to order λ or λ2 for the correlation functions and for the mass gap. All Osterwalder-Schrader axioms are satisfied except perhaps Euclidean (rotation) invariance.

AB - We use Schwinger-Dyson equations combined with rigorous "perturbation-theoretic" correlation inequalities to give a new and extremely simple proof of the existence and nontriviality of the weakly-coupled continuum φ{symbol}24 and φ{symbol}34 quantum field theories, constructed as subsequence limits of lattice theories. We prove an asymptotic expansion to order λ or λ2 for the correlation functions and for the mass gap. All Osterwalder-Schrader axioms are satisfied except perhaps Euclidean (rotation) invariance.

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A new proof of the existence and nontriviality of the continuum ϕ24 and ϕ34 quantum field theories

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