Abstract
A cluster expansion is proposed for the calculation of certain Green’s functions in field theory. The results presented are for λφ4 theory, expanded in the number of scalar closed loops through the introduction of the composite field, χ = i√λ/12 φ2. As an intermediate step, Feynman path integrals are used to perform the functional integration over the field degrees of freedom. The cluster expansion that results is equivalent to perturbation theory, but at lowest order sums up all the infrared behavior of the theory. Higher orders systematically include ultraviolet effects.
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