Renormalization group functions of the φ4 theory in the strong coupling limit: Analytical results
Renormalization group functions of the φ4 theory in the strong coupling limit: Analytical results
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强耦合极限下 φ4 理论的重正化群函数：解析结果
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
I. Suslov
中科院分区：
文献类型：
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作者：
I. Suslov
以往的尝试通过对扰动级数求和来重建φ4理论的Gell-Mann-Low函数β（g），给出了在极限g→∞中β（g）= β∞g的渐近行为，其中对空间维数d = 2，3，4，α = 1。可以假设，对于所有d值，渐近行为都是β（g）g。考虑零维的情况下，支持这一假设，并揭示了其外观的机制：它是与消失的功能积分之一。分析的推广证实了一般d维情形下的渐近行为β（g）g。其他重整化群函数的渐近行为是常数。讨论了φ4理论与零荷问题和平凡性的关系。
The previous attempts of reconstructing the Gell-Mann-Low function β(g) of the φ4 theory by summing perturbation series give the asymptotic behavior β(g) = β∞g in the limit g→∞, where α = 1 for the space dimensions d = 2, 3, 4. It can be hypothesized that the asymptotic behavior is β(g) ∼ g for all d values. The consideration of the zero-dimensional case supports this hypothesis and reveals the mechanism of its appearance: it is associated with vanishing of one of the functional integrals. The generalization of the analysis confirms the asymptotic behavior β(g) ∼ g in the general d-dimensional case. The asymptotic behaviors of other renormalization group functions are constant. The connection with the zero-charge problem and triviality of the φ4 theory is discussed.