Abstract
The formalism developed in a previous paper is applied to yield a phase cell cluster expansion for a hierarchical ø 43 model. The field is expanded into modes with specific renormalization group scaling properties. The present cluster expansion for a vacuum expectation value is formally the natural factorization of each term in the perturbation expansion into the contribution of modes connected to the variables in the expectation via interactions, and that of the complementary set. The expectation value is thus realized as a sum of contributions due tofinite subsets of the modes. We emphasize the following additional features:
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1)
Partitions of unity are not used.
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2)
There areessentially no cut-offs.
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3)
The expansion is developed directly, without an initial need to prove an ultraviolet stability bound, the most difficult part of the traditional approach.
Our main interest in the present phase cell cluster expansion is founded in the belief that it may be the right vehicle for proving the existence of a nontrivial four-dimensional field theory.
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Communicated by A. Jaffe
This work was supported in part by the National Science Foundation under Grant No. PHY 79-05688
On leave from Mathematics Department, Texas A&M University, College Station, TX77843, USA
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Battle, G.A., Federbush, P. A phase cell cluster expansion for a hierarchical Ø 43 model. Commun.Math. Phys. 88, 263–293 (1983). https://doi.org/10.1007/BF01209480
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DOI: https://doi.org/10.1007/BF01209480