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According to something called Haagís theorem there appears to be no known consistent formalism within which interacting quantum Öeld theory can be expressedî(p. 115).
"An interpretative introduction to quantum Field theory" by Teller (1995)
For the best explanation, see the section "How to stop worrying about Haag's theorem" in the book "The Conceptual Framework of Quantum Field Theory" by A. Duncan