Functional-integral representation of the Kadyshevsky perturbation expansion

Establish that the Kadyshevsky perturbation expansion is generated by the functional integral expression given in equation (C.11), with the normalization chosen so that the generating functional satisfies Z[0,0,0]=1.

Background

The paper develops a functional-integral formalism for Kadyshevsky field theory by introducing auxiliary quasi-particle fields whose contractions reproduce the ordering factors involving the time-like vector n^\mu. It defines free generating functionals for the scalar and quasi-particle sectors and then proposes an interacting generating functional obtained by applying functional derivatives representing the interaction Lagrangian.

The proposed formula is explicitly introduced as a conjecture rather than established as a theorem. If valid, functional differentiation of this expression would generate the generalized Wightman functions and thereby provide the perturbative Kadyshevsky graphs and their reduction formulas in a unified functional framework.