论文标题
HADAMARD国家关于全球双曲机空间的验量量子场理论
Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes
论文作者
论文摘要
根据Radzikowski的著名结果，在全球双曲线时空上的浪潮操作员是Hadamard形式的，如果它们是通过杰出参数的线性组合给出的，$ \ frac {i} {i} {2} {2} {2} {\ big big（\ wideteDe在Duistermaat -Hörmander的意义上，\ widetilde {g} _a- \ widetilde {g} _r \ big）$。灵感来自相应的高级和智障绿色操作员$ g_a，g_r $，bär，ginoux，ginoux，pfäffle2007，我们构建了剩下的两个绿色操作员$ g_f，g_f，g_ {af {af} $在哈达玛德系列方面。之后，我们提供了$ \ frac {i} {2} \ big（\ widetilde {g} _ {af} - \ widetilde {g} _ {f} \ big）$的全球构造，该$依赖于新技术，这些技术依赖于诸如papped cauchy问题的新技术，并使用了biSecting to new to bisogy and packing and packing and packing croment。这导致了Hadamard形式的全局两种形式，可以选择每种形式为Hadamard两点功能，即可以对光滑的部分进行调整，以使对称性和阳性条件完全满足。
According to Radzikowski's celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of Hadamard form iff they are given by a linear combination of distinguished parametrices $\frac{i}{2}\big(\widetilde{G}_{aF} - \widetilde{G}_{F} + \widetilde{G}_A - \widetilde{G}_R\big)$ in the sense of Duistermaat-Hörmander. Inspired by the construction of the corresponding advanced and retarded Green operator $G_A,G_R$ as done in Bär, Ginoux, Pfäffle 2007, we construct the remaining two Green operators $G_F, G_{aF}$ locally in terms of Hadamard series. Afterwards, we provide the global construction of $\frac{i}{2}\big(\widetilde{G}_{aF} - \widetilde{G}_{F}\big)$, which relies on new techniques like a well-posed Cauchy problem for bisolutions and a patching argument using Čech cohomology. This leads to global bisolutions of Hadamard form, each of which can be chosen to be a Hadamard two-point-function, i.e. the smooth part can be adapted such that, additionally, the symmetry and the positivity condition are exactly satisfied.
