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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.
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