Abstract
Functional integrals that are formally related to the average correlation functions of a classical field theory in the presence of random external sources are given a rigorous meaning. Their dimensional reduction to the Schwinger functions of the corresponding quantum field theory in two fewer dimensions is proven. This is done by reexpressing those functional integrals as expectations of a supersymmetric field theory. The Parisi-Sourlas dimensional reduction of a supersymmetric field theory to a usual quantum field theory in two fewer dimensions is proven.
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Communicated by A. Jaffe
Partially supported by the NSF under grant MCS-8301889
Partially supported by FAPESP
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Klein, A., Landau, L.J. & Perez, J.F. Supersymmetry and the Parisi-Sourlas dimensional reduction: A rigorous proof. Commun.Math. Phys. 94, 459–482 (1984). https://doi.org/10.1007/BF01403882
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DOI: https://doi.org/10.1007/BF01403882