量子场论中的局域因果结构、Hadamard态和局域协变性原理
Local causal structures, Hadamard states and the principle of local covariance in quantum field theory
摘要：
在代数表述的框架下，我们讨论和分析了强因果时空中实标量量子场论局域结构的一些新特征。特别是，我们使用的指数映射的属性，以建立一个本地版本的批量到边界的对应。主体是一个合适的子集的测地线附近的任何，但不固定点p的底层背景，而边界是一个未来的光锥的一部分，有p作为自己的尖端。在这个制度中，我们提供了一个新的概念，扩展 *-代数的威克多项式在说锥，一方面，我们证明了它包含的信息，通过一个内射 *-同态的散装对应，而另一方面，我们关联到它的一个杰出的状态，其拉回的散装是阿达玛形式。如果使用指数映射和光锥的普适性质来表明，对于任意两个给定的背景M和M'以及任意两个点的测地邻域的任意两个子集，可以设计上述过程，使得边界扩展代数通过限制同态相关，则会出现这种观点的主要优点。这允许在两个时空中的边界状态的拉回，因此，建立了一个机器，允许在M和M '中的局部场观测的期望值的比较。
英文摘要：
In the framework of the algebraic formulation, we discuss and analyse some new features of the local structure of a real scalar quantum field theory in a strongly causal spacetime. In particular we use the properties of the exponential map to set up a local version of a bulk-to-boundary correspondence. The bulk is a suitable subset of a geodesic neighbourhood of any but fixed point p of the underlying background, while the boundary is a part of the future light cone having p as its own tip. In this regime, we provide a novel notion for the extended *-algebra of Wick polynomials on the said cone and, on the one hand, we prove that it contains the information of the bulk counterpart via an injective *-homomorphism while, on the other hand, we associate to it a distinguished state whose pull-back in the bulk is of Hadamard form. The main advantage of this point of view arises if one uses the universal properties of the exponential map and of the light cone in order to show that, for any two given backgrounds M and M' and for any two subsets of geodesic neighbourhoods of two arbitrary points, it is possible to engineer the above procedure such that the boundary extended algebras are related via a restriction homomorphism. This allows for the pull-back of boundary states in both spacetimes and, thus, to set up a machinery which permits the comparison of expectation values of local field observables in M and M'.
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