Olbertian partition function in scalar field theory

The Olbertian partition function is reformulated in terms of continuous (Abelian) fields described by the Landau-Ginzburg action, respectively Hamiltonian. In order do make some progress, the Gaussian approximation to the partition function is transformed into the Olbertian prior to adding the quartic Landau-Ginzburg term in the Hamiltonian. The final result is provided in the form of an expansion suitable for application of diagrammatic techniques once the nature of the field is given, i.e. once the field equations are written down such that the interactions can be formulated.