Consistent use of effective potentials
Consistent use of effective potentials
复制标题
持续利用有效潜力
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
M. Schwartz
中科院分区：
文献类型：
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作者：
Anders Andreassen;William Frost;M. Schwartz
众所周知，有效电位可以与量规有关，而它们在极值处的值应该是量规不变的。不幸的是，在微扰理论中建立这种不变性并不简单，因为来自任意高阶回路的贡献可能具有相同的大小。我们证明了在无质量标量QED中，可以（而且必须）对无限类环路求和，以给出其最小位能的规范不变值。此外，我们证明了确切的势取决于计算它的尺度和场的归一化，但真空能与此无关。利用这些见解，我们提出了一种从摄动理论中逐阶自洽的有效势中提取物理量的方法，包括对重整化群的改进。
It is well known that effective potentials can be gauge-dependent while their values at extrema should be gauge-invariant. Unfortunately, establishing this invariance in perturbation theory is not straightforward, since contributions from arbitrarily high- order loops can be of the same size. We show in massless scalar QED that an infinite class of loops can be summed (and must be summed) to give a gauge invariant value for the potential at its minimum. In addition, we show that the exact potential depends on both the scale at which it is calculated and the normalization of the fields, but the vacuum energy does not. Using these insights, we propose a method to extract some physical quantities from effective potentials which is self-consistent order-by-order in perturbation theory, including improvement with the renormalization group.