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Perturbation theory of Wightman functions

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Abstract

A perturbative expansion of the Wightman functions, and more generally of vacuum expectation values of products of time-ordered and anti-time-ordered products, is derived for Ф 44 field theory. The result is expressed as a sum over generalized Feynman graphs. The derivation is based exclusively on the equation of motion and the Wightman axioms. Neither canonical commutation relations nor asymptotic conditions are needed at any point. In the zero-mass case the individual graphs are infrared divergent, but the sum over all graphs of a given order is convergent.

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Communicated by K. Gawedzki

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Steinmann, O. Perturbation theory of Wightman functions. Commun.Math. Phys. 152, 627–645 (1993). https://doi.org/10.1007/BF02096621

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  • DOI: https://doi.org/10.1007/BF02096621

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