  In this thesis an iterative scheme for the construction of operator product
expansion (OPE) coefficients is applied to determine low order coefficients in
perturbation theory for a specific toy model. We use the approach to quantum
field theory proposed by S. Hollands [arXiv:0802.2198], which is centered
around the OPE and a number of axioms on the corresponding OPE coefficients.
This framework is reviewed in the first part of the thesis.
  In the second part we apply an algorithm for the perturbative construction of
OPE coefficients to a toy model: Euclidean $\varphi^6$-theory in 3-dimensions.
Using a recently found formulation in terms of vertex operators and a
diagrammatic notation in terms of trees [arXiv:0906.5313v1], coefficients up to
second order are constructed, some general features of coefficients at
arbitrary order are presented and an exemplary comparison to the corresponding
customary method of computation is given.
