Dirac算子的迹恒等式与微扰展式的一个关系

Relationship between Dirac Operator's Trace Identity and Disturbance Expansion of Eigenvalue's Infinitesima

经典Dirac算子在微扰因子μ的扰动下,如果特征值能展为微扰参数的幂级数λn(μ)=λn(0)+μλn1+μ2λn2+…,利用Green函数的微扰展开式和一个积分恒等式,可得到迹恒等式的正则部分就是此展式的前3项,即∑∞(λn(μ)-λn(0)-μλn1-μ2λn2)=0,并且对特征值的正整幂λnσ也有类似现象.

Under the disturbance of μ,if the classical Dirac operator can develop power series：λn（μ）=λn（0）＋μλn1＋μ2λn2＋…,the trace＇s regular parts that are just this expansion＇s prefix three part will be obtained,that is ∑∞n=-∞（λn（μ）-λn（0）-μλn1-μ2λn2）=0,using Green function＇s infinitesimal distrubance expansion and one integral identity.And there is a similar result of λσn.