A convergent expansion about mean field theory: I. The expansion |
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Authors: | James Glimm Arthur Jaffe Thomas Spencer |
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Institution: | Rockefeller University, New York, New York 10021 USA;Harvard University, Cambridge, Massachusetts 02138 USA;Rockefeller University, New York, New York 10021 USA |
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Abstract: | We give a convergent expansion for nearly Gaussian quantum field theory in the multiphase region. The expansion combines (1) an expansion in phase boundaries, (2) a cluster expansion, and (3) a perturbation expansion to isolate dominant behavior. We study in detail the ground state of the (φ)2 = (λφ4 ? φ2 ? μφ)2 model, with ∥ μ ∥ ? λ2 ? 1. The ground state is close to the classical free field, obtained by replacing (φ) by the quadratic mean field polynomial c(φ), tangent to at a global minimum. Selecting one minimum gives a pure phase (ergodic ground state) satisfying the Wightman-Osterwalder-Schrader axioms with a positive mass. We also establish analyticity in λ for μ = 0 in the sector ∥ Im λ ∥ < ? Re λ ? 1, for ? ? 1. |
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