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Quantum field theories in all dimensions. (English) Zbl 0851.46051
We exhibit a large class of hermitian scalar field theories satisfying the Wightman axioms. For each $$d>0$$, and each polynomial $$P$$, we exhibit a collection of theories which are loosely but legitimately based on a $$P(\varphi)$$ interaction in $$d$$ space dimensions. One of the features of the construction is that the Wightman $$n$$-point function of each theory is a sum of finitely many integrals associated with “Feynman-like” graphs. Thus, it is in closed form.

##### MSC:
 46N50 Applications of functional analysis in quantum physics 81T08 Constructive quantum field theory 81T10 Model quantum field theories
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##### References:
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