The Hadamard Construction of Green's Functions on a Curved Space‐Time with Symmetries

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Abstract
The Hadamard constituents of Green's functions for a ζ‐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 transport 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.