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We identify a nontrivial yet tractable quantum field theory model withspace/time anisotropic scale invariance, for which one can exactly computecertain four-point correlation functions and their decompositions via theoperator-product expansion(OPE). The model is the Calogero model,non-relativistic particles interacting with a pair potential$\frac{g}{|x-y|^2}$ in one dimension, considered as a quantum field theory inone space and one time dimension via the second quantisation. This model hasthe anisotropic scale symmetry with the anisotropy exponent $z=2$. The symmetryis also enhanced to the Schr\"odinger symmetry. The model has one couplingconstant $g$ and thus provides an example of a fixed line in therenormalisation group flow of anisotropic theories.  We exactly compute a nontrivial four-point function of the fundamental fieldsof the theory. We decompose the four-point function via OPE in two differentways, thereby explicitly verifying the associativity of OPE for the first timefor an interacting quantum field theory with anisotropic scale invariance. Fromthe decompositions, one can read off the OPE coefficients and the scalingdimensions of the operators appearing in the intermediate channels. One of thedecompositions is given by a convergent series, and only one primary operatorand its descendants appear in the OPE. The scaling dimension of the primaryoperator we computed depends on the coupling constant. The dimension correctlyreproduces the value expected from the well-known spectrum of the Calogeromodel combined with the so-called state-operator map which is valid fortheories with the Schr\"odinger symmetry. The other decomposition is given byan asymptotic series. The asymptotic series comes with exponentially smallcorrection terms, which also have a natural interpretation in terms of OPE.

Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance