类光超曲面的Hadamard态
Hadamard States From Light-like Hypersurfaces
摘要：
这本书提供了一个相当独立的调查建设阿达玛国家的标量场理论在一大类著名的时空，拥有一个（共形）轻般的边界。前两个部分着重于解释这个主题的一些介绍性方面，并提供相关的几何背景材料。渐近平坦的时空和膨胀的宇宙与宇宙视界的概念进行了详细分析，特别注意渐近对称性的表征。在书的中心部分，量子化的一个真正的标量场理论对这样一类的背景下讨论的框架内的代数量子场论。随后，它是解释如何有可能编码的信息的可观的理论在第二个，辅助对应，这是直接建立在共形（零）边界。这个过程，被称为体-边界对应，有一个净优势，允许识别一个独特的状态的理论在边界上，它承认一个对应的体时空，这是自动阿达玛形式。在最后一部分的书，一些应用这些国家进行了讨论，特别是建设的代数威克多项式。这本书的主要目的是，但不是唯一的，在弯曲的背景上的量子场论的数学公式感兴趣的读者群。
英文摘要：
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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