论文标题
大规模标量场理论的最简单最小减法
The simplest minimal subtraction for massive scalar field theory
论文作者
论文摘要
提出了大规模λϕ4标量场理论的最简单最小减法方法。我们利用单粒子不可约的顶点零件框架仅处理可以将其重新归一化的原始发散框架处理。我们给出了带有Minkowski或Euclidean签名的时空度量张量的统一描述。两点顶点部分的剩余图中的部分P操作用于摆脱其重叠的差异。我们展示了参数解离如何有效地消除了在两点顶点部分图中执行部分P的局部-P操作后，平方裸体质量系数的外部动量依赖性。指出了这种方法与无数理论中最小的减法方案的相似之处。我们使用最小的减法参数得出Callan-Symanzik方程，并讨论紫外线区域的缩放限制。我们采用该方法来确定O（n）内部对称性的关键指数，至少具有平坦的欧几里得指标，并与文献中所有先前的结果找到完美的一致性。
The simplest minimal subtraction method for massive λϕ4 scalar field theory is presented. We utilize the one-particle irreducible vertex parts framework to deal only with the primitive divergent ones that can be renormalized multiplicatively. We give a unified description for spacetime metric tensor with either Minkowski or Euclidean signature.The partial-p operation in the remaining diagrams of the two-point vertex part are used to get rid of its overlapping divergences. We show how the parametric dissociation transform effectively eliminates the external momentum dependence of the coefficient of the squared bare mass after performing the partial-p operation in the two-point vertex part diagrams. The resemblance of this method with a minimal subtraction scheme in the massless theory is pointed out. We derive the Callan-Symanzik equations using minimal subtraction arguments and discuss the scaling limit in the ultraviolet region. We apply the method to determine critical exponents for an O(N) internal symmetry at least up to two-loop order with a flat Euclidean metric and find perfect agreement with all previous results in the literature.
