The result of removing of heavy non-equal mass particles from the theory can be described, at low energy, by the effective action, which is a series in inverse-square powers of the mass. We propose a new efficient tool to calculate the leading terms of this series based on the Schwinger proper-time method. Unequal masses give rise to a large number of effective vertices describing the explicit flavor symmetry breaking effects with well-defined coupling constants. Our method is pertinent to the theory with explicit and spontaneous chiral symmetry breaking, chiral gauge theory, standard and beyond standard model effective field theory, the theory of critical phenomena, cosmology, etc.

可以通过有效作用以低能量描述从理论上去除重的不等重粒子的结果，该作用是质量的反平方幂。我们提出了一种新的高效工具，可以基于Schwinger适当时间方法来计算该系列的首付款项。质量不相等会产生大量有效顶点，这些顶点描述具有明确定义的耦合常数的显着的风味对称性破坏效果。我们的方法与具有明确和自发的手性对称性破坏理论，手性规范理论，标准和超标准模型有效场论，临界现象，宇宙论等相关。