  This book provides a rather self-contained survey of the construction of
Hadamard states for scalar field theories in a large class of notable
spacetimes, possessing a (conformal) light-like boundary. The first two
sections focus on explaining a few introductory aspects of this topic and on
providing the relevant geometric background material. The notions of
asymptotically flat spacetimes and of expanding universes with a cosmological
horizon are analysed in detail, devoting special attention to the
characterization of asymptotic symmetries. In the central part of the book, the
quantization of a real scalar field theory on such class of backgrounds is
discussed within the framework of algebraic quantum field theory. Subsequently
it is explained how it is possible to encode the information of the observables
of the theory in a second, ancillary counterpart, which is built directly on
the conformal (null) boundary. This procedure, dubbed bulk-to-boundary
correspondence, has the net advantage of allowing the identification of a
distinguished state for the theory on the boundary, which admits a counterpart
in the bulk spacetime which is automatically of Hadamard form. In the last part
of the book, some applications of these states are discussed, in particular the
construction of the algebra of Wick polynomials. This book is aimed mainly, but
not exclusively, at a readership with interest in the mathematical formulation
of quantum field theory on curved backgrounds.
