用狄拉克δ函数近似值法处理光子真空极化的紫外发散问题

Treatment of the integral divergence in computations of vacuum polarization for photons with the method of approximate values of Dirac δ function

用狄拉克δ函数近似值法的扩展规则,取以紫外发散为特征的双光子真空极化(光子自能)系统为例,导出了正规化公式,与文献中由空-时维度法导得的公式相似.公式以(n↑)为正规化参数,与4维动量有相同的量纲.由此进一步确定系统的树枝图及1-圈图各自的振幅、相对项振幅及系统的重整化振幅,后者与文献中的完全相同.最后确定了相对项拉氏密度.

With the extension rule of the method of approximate values of Dirac δ function a new regularization equation of vacuum polarization （self-energy） for photons is developed with （n ↑ ） as the regularization parameter which has the same dimension as 4-momentum, the equation is similar to that in reference books such as that of dimensional regularization. The separate amplitudes of tree-level and l-loop contributions of the system are determined, the counterterm and the renormalized amplitudes are further derived while the latter is all the same to that in reference books. Finally the counterterm Lagrangian is determined.