本文研究了Rindler空间上的二维Maxwell系统，其度量为ds ^2 = \exp（2 α）\cdot（dη^2-d η ^2）.与度规为ds^2= dt^2-dx^2的闵可夫斯基时空相比，我们发现真空能有一个额外的贡献。这种额外的贡献可以追溯到非物理的自由度（在闵可夫斯基空间中）。出现这种效应的技术原因是Bogolubov系数的性质，它混合了正频率和负频率模式。相应的混合是不可避免的，因为正频模关于Minkowski时间t的投影和正频模关于Rindler观测者的固有时间η的投影是不等价的。在Minkowski空间中保持的非物理自由度的精确消去在Rindler空间中不成立。在BRST方法中，这种效应表现为L和R部分中存在BRST电荷密度。Minkowski真空中的惯性观测器|0>观察到一个没有净BRST电荷的宇宙，这只是两者之间相互抵消的结果。然而，林德勒的观测者无法进入整个时空，他们会看到一个净的BRST电荷。在这方面，这种效应类似于Unruh效应。该效应本质上是红外（IR）的，并且对地平线和/或边界敏感。我们把这种额外的能量解释为当虚自由度不能传播，但仍然对真空能量有贡献时，“虚凝聚”的形成。在这个简单的二维模型中的精确计算支持了[1]中提出的幽灵贡献可能是导致在四维FLRW宇宙中观测到的暗能量的原因。
英文摘要：
We consider 2d Maxwell system defined on the Rindler space with metric ds^2=\exp(2aξ)\cdot(dη^2-dξ^2) with the goal to study the dynamics of the ghosts. We find an extra contribution to the vacuum energy in comparison with Minkowski space time with metric ds^2= dt^2-dx^2. This extra contribution can be traced to the unphysical degrees of freedom (in Minkowski space). The technical reason for this effect to occur is the property of Bogolubov's coefficients which mix the positive and negative frequencies modes. The corresponding mixture can not be avoided because the projections to positive -frequency modes with respect to Minkowski time t and positive -frequency modes with respect to the Rindler observer's proper time ηare not equivalent. The exact cancellation of unphysical degrees of freedom which is maintained in Minkowski space can not hold in the Rindler space. In BRST approach this effect manifests itself as the presence of BRST charge density in L and R parts. An inertial observer in Minkowski vacuum |0> observes a universe with no net BRST charge only as a result of cancellation between the two. However, the Rindler observers who do not ever have access to the entire space time would see a net BRST charge. In this respect the effect resembles the Unruh effect. The effect is infrared (IR) in nature, and sensitive to the horizon and/or boundaries. We interpret the extra energy as the formation of the "ghost condensate" when the ghost degrees of freedom can not propagate, but nevertheless do contribute to the vacuum energy. Exact computations in this simple 2d model support the claim made in [1] that the ghost contribution might be responsible for the observed dark energy in 4d FLRW universe.
