Quantum field theories in all dimensions (Q1918114)

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.