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SpringerBriefs in Mathematical Physics

Hadamard States from Light-like Hypersurfaces

Authors: Dappiaggi, Claudio, Moretti, Valter, Pinamonti, Nicola

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  • ISBN 978-3-319-64343-4
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Softcover $54.99
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About this book

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.

Table of contents (5 chapters)

  • Introduction

    Dappiaggi, Claudio (et al.)

    Pages 1-10

  • General Geometric Setup

    Dappiaggi, Claudio (et al.)

    Pages 11-33

  • Quantum Fields in Spacetimes with Null Surfaces

    Dappiaggi, Claudio (et al.)

    Pages 35-56

  • Boundary-Induced Hadamard States

    Dappiaggi, Claudio (et al.)

    Pages 57-96

  • Wick Polynomials and Extended Observables Algebras

    Dappiaggi, Claudio (et al.)

    Pages 97-106

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-64343-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-64342-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Hadamard States from Light-like Hypersurfaces
Authors
Series Title
SpringerBriefs in Mathematical Physics
Series Volume
25
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-64343-4
DOI
10.1007/978-3-319-64343-4
Softcover ISBN
978-3-319-64342-7
Series ISSN
2197-1757
Edition Number
1
Number of Pages
VIII, 106
Number of Illustrations and Tables
2 b/w illustrations
Topics