论文标题
精确的重新归一化组和尺寸正则化
The exact renormalization group and dimensional regularization
论文作者
论文摘要
确切的重归其化组（ERG）是通过特定的动量整合度量来实施自由度的分解的。该措施的定义涉及将这种分解过程与现场理论计算中使用的维数正则化技术联系起来的分布。如果尺寸为d = 4-ε，则显示该方案中标量场理论的ERG方程的一个环溶液与限制μ\ to0中的尺寸正则扰动场理论计算相吻合，如果所使用的比例参数μ和ε在使用。通常，在该方案中，当μ\ to0与田间理论中出现的完整示意贡献和该理论的完整示意贡献时，ERG方程的解决方案的解决方案是重合的。另外，还考虑了非扰动近似。该近似值包括ERG方程的截断，通过低动量扩展会导致合理的结果。
The exact renormalization group (ERG) is formulated implementing the decimation of degrees of freedom by means of a particular momentum integration measure. The definition of this measure involves a distribution that links this decimation process with the dimensional regularization technique employed in field theory calculations. Taking the dimension d=4-ε, the one loop solutions to the ERG equations for the scalar field theory in this scheme are shown to coincide with the dimensionally regularized perturbative field theory calculation in the limit μ\to0, if a particular relation between the scale parameter μand εis employed. In general, it is shown that in this scheme the solutions to the ERG equations for the proper functions coincide when μ\to0 with the complete diagrammatic contributions appearing in field theory for these functions and this theory, provided that exact relations between μand εhold. In addition a non-perturbative approximation is considered. This approximation consists in a truncation of the ERG equations, which by means of a low momentum expansion leads to reasonable results.
