Quest for particles production in the plane gravitational wave spacetime

Massless vector and scalar Green's functions are obtained in closed form for a plane gravitational wave spacetime using three independent methods: direct solution of the Green-function equation and construction via the DeWitt and Hadamard recursive schemes. The results coincide exactly with the DeWitt--Schwinger expansion, indicating no massless particles production in this background. Contrasting interpretations, based on Bogolyubov coefficient calculations predicting massless particle creation, are also addressed.