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Construction and Borel summability of infrared Φ 44 by a phase space expansion

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Abstract

We construct the thermodynamic limit of the critical (massless) φ4 model in 4 dimensions with an ultraviolet cutoff by means of a “partly renormalized” phase space expansion. This expansion requires in a natural way the introduction of effective or “running” constants, and the infrared asymptotic freedom of the model, i.e. the decay of the running coupling constant, plays a crucial rôle. We prove also that the correlation functions of the model are the Borel sums of their perturbation expansion.

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Communicated by K. Osterwalder

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Feldman, J., Magnen, J., Rivasseau, V. et al. Construction and Borel summability of infrared Φ 44 by a phase space expansion. Commun.Math. Phys. 109, 437–480 (1987). https://doi.org/10.1007/BF01206146

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