I wrote this book for Japanese, because in Japan there is no book of quantum field theory in curved spacetime. However, I translate Japanese book for English. And the reason to write this book is there is no book that writes the derivations of Green function. We should read papers from now on. However, in this book, I write the derivations of Green function.
This book mainly depend on review of L.H.Ford and the book of Birrell and Davies and my doctor thesis. However, I discuss conformal coupling and the derivation of Green function and black hole evaporation. The black hole evaporation is solved by Sawayama in 2006. And section 6 is mainly depended on my paper. The problem of black hole evaporation is difficult, because we should solve field equations i.e. forth order partial differential equations. However, I solved this problem by another method that is same as solving field equation. The black hole evaporation is advocated by Hawking in 1975. He said black hole may be vanishing. However, it is difficult problem, because we should solve field equations.
To read this book we know quantum field theory and general relativity.