Phase transitions and the Universe
Phase transitions and the Universe
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相变和宇宙
DOI：
10.1070/pu1982v025n03abeh004529
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发表时间：
1982
期刊：
影响因子：
2.7
通讯作者：
A. Polyakov
中科院分区：
文献类型：
--
作者：
A. Polyakov
爱因斯坦方程中的宇宙学项必然来自这样一个事实，即真空由于零点振荡而具有非零的能量密度。如果用特征强子质量来估计这个能量密度，那么宇宙常数A就会得到一个巨大的值。此外，为了与红移的实验数据一致，A的容许值必须小于自然强子估计的10”130。从表面上看，必须存在一种补偿机制，使真空的能量密度降低到零。这项工作的目的就是要找到这样一种机制，要解决这个问题，首先要确定它的正确提法。问题是能量一般被定义在一个常数之内，因此这个常数的选择似乎不清楚。然而，如果我们不研究能量密度，而是研究引力场传播的有效方程，那么一切福尔斯就都清楚了。所谓”有效”一词，我们指的是由爱因斯坦的原始理论作为红外量子重整化的结果而产生的方程。重要的是要认识到，一般来说，在任何理论中观察到的经典动力学都是由有效方程而不是由原始方程决定的。在某些情况下（例如，在杨-米尔斯理论中），红外重整化并不完全破坏原始的经典理论。在我们感兴趣的问题-爱因斯坦的理论与裸露的宇宙学常数-红外归一化的作用是比较温和的。它将表明，他们导致消失的物理宇宙常数，而不影响爱因斯坦的方程本身。
The cosmological term in Einstein's equations would necessarily arise from the fact that the vacuum has a nonzero energy density because of the zero-point oscillations. If this energy density is estimated using the characteristic hadronic masses, a colossal value is obtained for the cosmological constant A. Moreover, for consistency with the experimental data on the red shift, the admissible value of A must be smaller than 10" 130 of the natural hadronic estimate. To all appearances, there must exist a compensation mechanism which reduces the energy density of the vacuum to zero. The objective of this work is to find such a mechanism.To solve this problem, we must first determine its correct formulation. The point is that energy is in general defined to within a constant, and therefore the choice of this constant seems unclear. However, everything falls into place if we study not the energy density, but the effective equations for the propagation of a gravitational field. By the word" effective" we mean the equations which arise from the original theory of Einstein as a result of infrared quantum renormalizations. It is very important to realize that in general the observed classical dynamics in any theory is determined by the effective equations rather than by the original ones. In certain cases (for example, in the Yang-Mills theory), the infrared renormalizations do not completely destroy the original classical theory. In the problem of interest to us—Einstein's theory with the bare cosmological constant—the role of the infrared normalizations is more modest. It will be shown that they lead to vanishing of the physical cosmological constant without affecting Einstein's equations themselves.