反射壁附近有质量标量场的局域热行为
Local thermal behaviour of a massive scalar field near a reflecting wall
摘要：
在无限大平面狄利克雷壁附近和无限大平面诺依曼壁附近，确定了有限温度下中性质量标量场应力-能量-动量张量的均方涨落和期望值.平坦背景具有任意维数，并且场任意耦合到消失曲率。结果表明，与真空的贡献，热的贡献是免费的边界发散，和附近的狄利克雷壁的标量场的热行为有很大的不同，从附近的诺依曼壁。远离墙壁的研究揭示了一个本地版本的降维，即，熟悉的黑体表达式的修正是线性的温度，与相应的系数只给出在真空期望值的背景下，少一个维度。结果表明，这种修正是“经典的”（即，不依赖于普朗克常数），只有当标量场是无质量的。一个自然的猜想是，“局部降维”是普遍的，因为它适用于无质量和有质量的场，而不管边界条件如何。
英文摘要：
The mean square fluctuation and the expectation value of the stress-energy-momentum tensor of a neutral massive scalar field at finite temperature are determined near an infinite plane Dirichlet wall, and also near an infinite plane Neumann wall. The flat background has an arbitrary number of dimensions and the field is arbitrarily coupled to the vanishing curvature. It is shown that, unlike vacuum contributions, thermal contributions are free from boundary divergences, and that the thermal behaviour of the scalar field near a Dirichlet wall differs considerably from that near a Neumann wall. Far from the wall the study reveals a local version of dimensional reduction, namely, corrections to familiar blackbody expressions are linear in the temperature, with the corresponding coefficients given only in terms of vacuum expectation values in a background with one less dimension. It is shown that such corrections are "classical" (i.e., not dependent on Planck's constant) only if the scalar field is massless. A natural conjecture that arises is that the "local dimensional reduction" is universal since it operates for massless and massive fields alike and regardless of the boundary conditions.
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