论文标题
标量辐射的局部热行为的歧义在一维盒中
Ambiguities in the local thermal behavior of the scalar radiation in one-dimensional boxes
论文作者
论文摘要
本文在计算中的某些歧义中报告了集合平均值$ \左<t_μ_ν\右> $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $在平面时段的一维盒中任意耦合的无质量标量盒的压力 - 能量量。该研究介绍了一个具有周期性边界条件（圆圈）的盒子和带有反射边缘的框（带有Dirichlet或Neumann的边界条件在端点处）。 $ \左<t^μ^ν\右> $的表达式是从有限温度的绿色功能中获得的。在附录中，为了控制典型的两个维度的差异，这些绿色功能是针对具有任意数量的维度和任意质量标量字段的相关背景计算的，并专门针对文本至两个维度和无质量字段。歧义是由于并非绝对收敛的双重系列的$ \左<t^μ^ν\右> $出现。评估两个相关总和的顺序，导致每种类型的盒子都有两种不同的热力学。在一个圆的情况下，歧义性对应于文献中的经典争议，是否应在分区函数的计算中考虑零模式贡献。对于具有反射边缘的盒子，这会导致热力学之一对应于总能量（通过在空间上整合非均匀能量密度来获得的总能量），这不取决于预期的曲率耦合参数$ξ$；而其他热力学奇怪地对应于$ξ$的总能量。人们考虑了热力学要求（例如本地和全球稳定性）及其对$ξ$值的限制。
This paper reports certain ambiguities in the calculation of the ensemble average $\left<T_μ_ν\right>$ of the stress-energy-momentum tensor of an arbitrarily coupled massless scalar field in one-dimensional boxes in flat spacetime. The study addresses a box with periodic boundary condition (a circle) and boxes with reflecting edges (with Dirichlet's or Neumann's boundary conditions at the endpoints). The expressions for $\left<T^μ^ν\right>$ are obtained from finite-temperature Green functions. In an appendix, in order to control divergences typical of two dimensions, these Green functions are calculated for related backgrounds with arbitrary number of dimensions and for scalar fields of arbitrary mass, and specialized in the text to two dimensions and for massless fields. The ambiguities arise due to the presence in $\left<T^μ^ν\right>$ of double series that are not absolutely convergent. The order in which the two associated summations are evaluated matters, leading to two different thermodynamics for each type of box. In the case of a circle, it is shown that the ambiguity corresponds to the classic controversy in the literature whether or not zero mode contributions should be taken into account in computations of partition functions. In the case of boxes with reflecting edges, it results that one of the thermodynamics corresponds to a total energy (obtained by integrating the non homogeneous energy density over space) that does not depend on the curvature coupling parameter $ξ$ as expected; whereas the other thermodynamics curiously corresponds to a total energy that does depend on $ξ$. Thermodynamic requirements (such as local and global stability) and their restrictions to the values of $ξ$ are considered.
