Theoretical Physics Group, Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom.
Phys Rev Lett. 2018 Jun 29;120(26):261601. doi: 10.1103/PhysRevLett.120.261601.
We consider relativistic (2+1)-dimensional quantum field theories (QFTs) on a product of time with a two-space and study the vacuum free energy as a functional of the temperature and spatial geometry. We focus on free scalar and Dirac fields on arbitrary perturbations of flat space, finding that the free energy difference from flat space is finite and always negative to leading order in the perturbation. Thus, free (2+1)-dimensional QFTs appear to always energetically favor a crumpled space on all scales; this is true both as a purely quantum effect at zero temperature and as a purely thermal effect at high temperature. Importantly, we show that this quantum effect is non-negligible for the relativistic Dirac degrees of freedom on monolayer graphene even at room temperature, so we argue that this vacuum energy effect should be included for a proper analysis of the equilibrium configuration of graphene or similar materials.
我们研究了时间与二维空间乘积上的相对论（2+1）-维量子场论（QFT），并研究了真空自由能作为温度和空间几何的函数。我们专注于任意扰动的平坦空间上的自由标量和狄拉克场，发现从平坦空间的自由能差在扰动的主要阶次上是有限的且总是负的。因此，自由（2+1）-维 QFT 在所有尺度上似乎总是在能量上有利于卷曲的空间；这既是在零温度下的纯量子效应，也是在高温下的纯热效应。重要的是，我们表明，即使在室温下，单层石墨烯上的相对论狄拉克自由度的这种量子效应也不可忽略，因此我们认为，对于石墨烯或类似材料的平衡构型的适当分析，应该包括这种真空能量效应。
