关于微局部分解与正规双曲算子Feynman Propagators的构造
On microlocalisation and the construction of Feynman Propagators for normally hyperbolic operators
AI总结：
本文提出全局双曲时空上正规双曲算子的全局微局部分解构造，推广了Duistermaat-Hörmander的Feynman propagators构造，并证明其满足反映Hadamard态存在性的正性性质。
摘要：
本文以几何术语给出了全局双曲时空上向量丛的正规双曲算子的全局微局部分解构造。作为应用，这被用来推广Duistermaat-Hörmander的Feynman propagators构造，从而纳入最重要的非标量几何算子。证明了对于关于Hermite丛度量为自伴的正规双曲算子，Feynman propagators可被构造为满足正性性质，这反映了弯曲时空中量子场论Hadamard态的存在性。我们还给出了全局双曲时空上Dirac-type算子Feynman propagators的更直接构造。尽管旋量上的自然丛度量不是正定的，在这种情况下，我们仍能给出满足正性的Feynman propagator的直接微局部构造。
英文摘要：
This article gives global microlocalisation constructions for normally hyperbolic operators on a vector bundle over a globally hyperbolic spacetime in geometric terms. As an application, this is used to generalise the Duistermaat-Hörmander construction of Feynman propagators, therefore incorporating the most important non-scalar geometric operators. It is shown that for normally hyperbolic operators that are selfadjoint with respect to a hermitian bundle metric, the Feynman propagators can be constructed to satisfy a positivity property that reflects the existence of Hadamard states in quantum field theory on curved spacetimes. We also give a more direct construction of the Feynman propagators for Dirac-type operators on a globally hyperbolic spacetime. Even though the natural bundle metric on spinors is not positive-definite, in this case, we can give a direct microlocal construction of a Feynman propagator that satisfies positivity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
