2017/01/01 by Claudio Dappiaggi, Valter Moretti, Nicola Pinamonti · 5 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Black Holes and Theoretical Physics #Boundary (topology) #Boundary conformal field theory #Cosmology and Gravitation Theories #Geometry #Hadamard transform #Mathematical analysis #Mathematical physics #Mathematics #Neumann boundary condition #Observable #Physics #Pure mathematics #Quantum mechanics #Robin boundary condition #Scalar (mathematics) #Scalar field #Spacetime #Theoretical physics #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/978-3-319-64343-4
published as SpringerBriefs in Mathematical Physics 2017 · 106 pages, 2 figures, to appear in SpringerBriefs in Mathematical Physics, references added
openalex publication_date 2017/01/01 · arxiv created 2017/07/02 · arxiv updated 2017/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.