强耦合极限下的B^4理论的重整化群函数：解析结果
Renormalization Group Functions of the ϕ^4 Theory in the Strong Coupling Limit: Analytical Results
摘要：
先前通过对微扰级数求和来重建Gell-Mann-Low函数β（g）的尝试给出了β（g）= β_ \infty g^α在极限g \to \infty中的渐近行为，其中对于空间维数d = 2，3，4，α \approx 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：它是与一个零的功能积分。分析的推广证实了一般d维情形下β（g）=β_ \infty g的渐近性态。其他重整化群函数的渐近行为是常数。讨论了零电荷问题与E1^4理论的平凡性之间的联系。
英文摘要：
The previous attempts of reconstructing the Gell-Mann-Low function β(g) of the ϕ^4 theory by summing perturbation series give the asymptotic behavior β(g) = β_\infty g^αin the limit g\to \infty, where α\approx 1 for the space dimensions d = 2,3,4. It can be hypothesized that the asymptotic behavior is β(g) ~ g for all values of d. The consideration of the zero-dimensional case supports this hypothesis and reveals the mechanism of its appearance: it is associated with a zero of one of the functional integrals. The generalization of the analysis confirms the asymptotic behavior β(g)=β_\infty g in the general d-dimensional case. The asymptotic behavior of other renormalization group functions is constant. The connection with the zero-charge problem and triviality of the ϕ^4 theory is discussed.
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