虚时表述中的场论
Field Theory in the Imaginary-time Formulation
摘要：
在场论中研究了时间-时间公式。利用Tolman-Escherfest关系和Wilson的重整化群方法，将Dirac和光子的拉格朗日量分别在时空中处理，并证明了它们在尺度变换下是不变的.利用泛函方法，可以导出实时和虚时轻子和光子的传播子。该理论是免费的紫外发散的积分范围内的时间，$(0,β\,]$，这是所需的KMS条件。单圈辐射修正的结果与QED的结果一致。与真空温度有关的重整化群方程没有给出朗道极点，并且在零温极限下的重整化系数与重整化的$\overline{MS}$方案相同。
英文摘要：
The imaginary-time formulation is investigated in the field theory. The Dirac and photon's Lagrangians are treated in the imaginary-time and space and are invariant under scale transformations, which are motivated by the Tolman-Ehrenfest relation and Wilson's approach in the renormalization group. With the functional approaches, the propagators of leptons and photons can be derived both for the real- and the imaginary-time. The theory is free of UV divergence in the integration range of the imaginary-time, $(0,β\,]$, which is required by the KMS condition. The results of one-loop radiative corrections are proved to be consistent with those in QED. The renormalization group equations with respect to vacuum's temperature give no Landau pole and show identical renormalization coefficients as those from the $\overline{MS}$ scheme of the renormalization in the limit of zero temperature.
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