标题： 能量-动量张量关联函数在欧几里得 $R^N$ 和 $AdS^N$ 空间中的量子场通过广义zeta函数方法 显示英文标题

标题： Stress-energy Tensor Correlators of a Quantum Field in Euclidean $R^N$ and $AdS^N$ spaces via the generalized zeta-function method

摘要： 在本文中，我们计算了与N维欧几里得空间和双曲空间（即反德西特（AdS）空间的欧几里得部分）具有广义耦合的宏观量子标量场的应力-能量双张量的真空期望值。这些关联函数也被称为噪声核，在随机引力的爱因斯坦-朗之万方程[1,2]中作为源项，这些方程描述了由半经典引力的半经典爱因斯坦方程所描述的平均场动力学之外的诱导度规涨落。由于这些空间是最大对称的，本征模式具有解析表达式，这有助于zeta函数的计算[3,4]。通过对[5]中引入的广义zeta函数进行二次泛函变分，我们得到了这两类时空的应力张量关联函数。对于直到11维的维度，给出了关联函数的短和大测地线距离极限。我们提到当前在早期宇宙宇宙学、黑洞物理和引力-流体对偶性中的研究问题，这些结果可以在此处得到有用的应用。 显示英文摘要

摘要： In this paper we calculate the vacuum expectation values of the stress-energy bitensor of a massive quantum scalar field with general coupling to N-dimensional Euclidean spaces and hyperbolic spaces which are Euclidean sections of the anti-de Sitter (AdS) spaces. These correlators, also known as the noise kernel, act as sources in the Einstein-Langevin equations of stochastic gravity [1,2] which govern the induced metric fluctuations beyond the mean-field dynamics described by the semiclassical Einstein equations of semiclassical gravity. Because these spaces are maximally symmetric the eigenmodes have analytic expressions which facilitate the computation of the zeta-function [3,4]. Upon taking the second functional variation of the generalized zeta function introduced in [5] we obtain the correlators of the stress tensor for these two classes of spacetimes. Both the short and the large geodesic distance limits of the correlators are presented for dimensions up to 11. We mention current research problems in early universe cosmology, black hole physics and gravity-fluid duality where these results can be usefully applied to.