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Renormalization of \Phi-derivable approximations in scalar field theories

机译:标量场理论中\ Phi近似的重整化

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摘要

We discuss the renormalization of \Phi-derivable approximations for scalar field theories. In such approximations, the self-energy is obtained as the solution of a self-consistent equation which effectively resums infinite subsets of diagrams of perturbation theory. We show that a consistent renormalization can be carried out, and we provide an explicit construction of the counterterms needed to eliminate the subdivergences. The counterterms are calculated from the solution of an auxiliary gap equation which determines the leading asymptotic part of the self-energy. This auxiliary gap equation may be chosen as the gap equation of the massless theory at zero temperature. We verify explicitly that the counterterms determined at zero temperature are sufficient to eliminate the divergences which occur in finite temperature calculations.
机译:我们讨论标量场理论的\ Phi近似的重整化。在这样的近似中,获得自能量作为自洽方程的解,该方程有效地恢复了扰动理论图的无限子集。我们表明可以执行一致的重新规范化,并且我们提供了消除相异性所需的反条件的明确构造。反条件是根据辅助间隙方程的解计算得出的,该方程确定了自能的前渐近部分。该辅助间隙方程可以被选择为零温度下无质量理论的间隙方程。我们明确验证了在零温度下确定的反条件足以消除有限温度计算中出现的差异。

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