论文标题
量子场理论的一般相对论
General Relativity from Quantum Field Theory
论文作者
论文摘要
一般相对论的量子场理论描述是一种现代的重力方法，其中带有Spin-2 Gravitons携带重力。在该理论的经典限制中，获得了爱因斯坦场方程所描述的一般相对论。该限制，其中经典的一般相对性来自量子场理论是本文的主题。 Schwarzschild-Tangherlini度量标准分析了任意时空维度（$ d $）中惯性点粒子的重力场。该度量与$ g_n $中所有订单的大规模标量相互作用的三分顶点函数与$ g_n $中的所有订单相互作用，并且计算了对此幅度的一环贡献，从中，$ g_n^2 $从中得出了$ g_n^2 $贡献对公制的贡献。 为了了解公制的量规依赖性，使用了协变量量规，引入了参数，$ξ$和固定量规函数$g_σ$。在经典限制中，固定函数被证明是坐标条件，$g_σ= 0 $。随着量规函数的使用，使用了一个新型的计量量，它依赖于任意参数$α$，并且使用了谐波和de donder仪表。 Feynman的重力场规则是得出的，重要的结果是协变量表中的重力传播器，也是N-Graviton顶点的一般公式，就爱因斯坦Tensor而言。 Feynman规则均用于从振幅中得出Schwarzschild-Tangherlini度量，并在计算对度量的一环校正中。 对度量标准的一环校正独立于协变量量规参数，$ξ$，并且满足量规条件$g_σ= 0 $，其中$g_σ$是$ gauges的家族，具体取决于$α$。在时空中，$ d = 5 $每个对数出现在位置空间中，并且根据冗余自由度分析了这种现象。
The quantum field theoretic description of general relativity is a modern approach to gravity where gravitational force is carried by spin-2 gravitons. In the classical limit of this theory, general relativity as described by the Einstein field equations is obtained. This limit, where classical general relativity is derived from quantum field theory is the topic of this thesis. The Schwarzschild-Tangherlini metric, which describes the gravitational field of an inertial point particle in arbitrary space-time dimensions, $D$, is analyzed. The metric is related to the three-point vertex function of a massive scalar interacting with a graviton to all orders in $G_N$, and the one-loop contribution to this amplitude is computed from which the $G_N^2$ contribution to the metric is derived. To understand the gauge-dependence of the metric, covariant gauge is used which introduces the parameter, $ξ$, and the gauge-fixing function $G_σ$. In the classical limit, the gauge-fixing function turns out to be the coordinate condition, $G_σ=0$. As gauge-fixing function a novel family of gauges, which depends on an arbitrary parameter $α$ and includes both harmonic and de Donder gauge, is used. Feynman rules for the graviton field are derived and important results are the graviton propagator in covariant gauge and a general formula for the n-graviton vertex in terms of the Einstein tensor. The Feynman rules are used both in deriving the Schwarzschild-Tangherlini metric from amplitudes and in the computation of the one-loop correction to the metric. The one-loop correction to the metric is independent of the covariant gauge parameter, $ξ$, and satisfies the gauge condition $G_σ=0$ where $G_σ$ is the family of gauges depending on $α$. In space-time $D=5$ a logarithm appears in position space and this phenomena is analyzed in terms of redundant gauge freedom.
