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arXiv 1808.09310hep-thgr-qc
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平面反射壁标量辐射的热力学

Thermodynamics of the scalar radiation in the presence of a reflecting plane wall

E. S. Moreira

备注：
13 pages, 1 figure, replaced by the published version which contains a review on quantum fields at finite temperature
发表信息：
Braz J Phys (2019) 49:449
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摘要：

本文进一步研究了在$N$维闵可夫斯基时空中，单反射平面壁的存在如何改变了无质量标量辐射热力学中的普朗克形式。这是以一种相当非传统的方式完成的，通过对空间上的能量密度积分，得到内能，并从内能中得到亥姆霍兹自由能。反射壁的建模是通过假设壁面上的Dirichlet或Neumann边界条件。发现当$N>2$在空间上积分时，消除了对曲率耦合参数$ξ$的依赖。但出乎意料的是，当$N=2$，内能和相应的热力学，结果是依赖于$ξ$。例如，对二维普朗克热容的修正是$\mp ξk_{B}$（狄利克雷为负，诺依曼为正）。这种依赖于$ξ$的其他方面也进行了讨论。结果与文献中关于反射壁（例如板）的相关设置的结果相矛盾，其中传统的（即，全局）方法来获得热力学。

英文摘要：

This paper investigates further how the presence of a single reflecting plane wall modifies the usual Planckian forms in the thermodynamics of the massless scalar radiation in $N$-dimensional Minkowski spacetime. This is done in a rather unconventional way by integrating the energy density over space to obtain the internal energy and from that the Helmholtz free energy. The reflecting wall is modelled by assuming the Dirichlet or the Neumann boundary conditions on the wall. It is found that when $N>2$ integration over space eliminates dependence on the curvature coupling parameter $ξ$. Unexpectedly though, when $N=2$, the internal energy and the corresponding thermodynamics turn out to be dependent on $ξ$. For instance, the correction to the two-dimensional Planckian heat capacity is $\mp ξk_{B}$ (minus for Dirichlet, plus for Neumann). Other aspects of this dependence on $ξ$ are also discussed. Results are confronted with those in the literature concerning related setups of reflecting walls (such as slabs) where conventional (i.e., global) approaches to obtain thermodynamics have been used.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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