The Hadamard construction of Green's functions on a curved space-time with symmetries

The Hadamard constituents of Green's functions for a ξ-parametrized generalization of the massless scalar d'Alembert equation to a curved space-time including the conformally invariant wave equation:the world function of space-time, the tansport scalar, and the tail-term coefficients, being simultaneously coefficients in the Schwinger-DeWitt expansion of the Feynman propagator for the corresponding invariant Klein-Gordon equation, are considered on a general static spherically symmetric and (2,2)-decomposable metric. The construction equations determining the Hadamard building elements are cast into a symmetry-adapted form and used to obtain, on a specific model metric, exact explicit solutions. (author)