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首页> 外文期刊>Annales Henri Poincare >Quantum Fields from Global Propagators on Asymptotically Minkowski and Extended de Sitter Spacetimes
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Quantum Fields from Global Propagators on Asymptotically Minkowski and Extended de Sitter Spacetimes

机译：来自全球传播者的量子领域在渐近的Minkowski和延伸的de Satter Spacetims

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We consider the wave equation on asymptotically Minkowski spacetimes and the Klein-Gordon equation on even asymptotically de Sitter spaces. In both cases, we show that the extreme difference of propagators (i.e., retarded propagator minus advanced, or Feynman minus anti-Feynman), defined as Fredholm inverses, induces a symplectic form on the space of solutions with wave front set confined to the radial sets. Furthermore, we construct isomorphisms between the solution spaces and symplectic spaces of asymptotic data. As an application of this result, we obtain distinguished Hadamard two-point functions from asymptotic data. Ultimately, we prove that non-interacting Quantum Field Theory on asymptotically de Sitter spacetimes extends across the future and past conformal boundary, i.e., to a region represented by two even asymptotically hyperbolic spaces. Specifically, we show this to be true both at the level of symplectic spaces of solutions and at the level of Hadamard two-point functions.
机译：我们考虑了渐近Minkowski Spacetims的波浪方程，甚至是渐近的de Satter空间上的Klein-Gordon方程。在这两种情况下，我们表明传播者的极端差异（即，延迟传播者减去高级，或Feynman减去Feyynman），定义为Fredholm逆，引起了伴有波前组的解决方案空间的辛形式，限制在径向上套。此外，我们在渐近数据的解决方案空间和辛空间之间构成同构。作为这种结果的应用，我们从渐近数据获得了与渐近数据的区别的Hadamard两点函数。最终，我们证明了在渐近的DE STERTIMES上的非交互量子场理论延伸到未来和过去的共形边界，即由两个甚至是渐近双曲线空间表示的区域。具体而言，我们在解决方案的辛空间水平和Hadamard两点函数的水平上表现出这一目标。

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