Semiclassical realization of infrared renormalons.
Semiclassical realization of infrared renormalons.
复制标题
红外重整子的半经典实现。
DOI：
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发表时间：
2012
影响因子：
8.6
通讯作者：
M. Unsal
中科院分区：
文献类型：
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作者：
P. Argyres;M. Unsal
量子场论中的微扰级数通常是发散的渐近级数，但它们也通常不是波莱尔可解的，因为它的可解级数是二义性的。这种不确定性与正真实的轴上Borel平面中的奇点有关。在量子力学中，存在这样的情况，即微扰论中出现的模糊性抵消了瞬子-反瞬子事件中类似的模糊性贡献。在渐近自由规范理论中，这种机制是不够的，因为微扰理论发展了与波莱尔平面中的奇点相关的模糊性，与瞬子事件实现的奇点相比，波莱尔平面中的奇点更接近原点约N倍（规范群的秩）。这些被称为IR重整化子极点，在R^{4}上它们不具有任何已知的半经典实现。利用R（3）× S（1）上的连续性，并将Bogomolny和Zinn-Justin的工作推广到QFT，我们确定了鞍点场组态，例如，bion-antibion事件，对应于Borel平面中的奇点，其比Borel平面中的四维瞬子-反瞬子奇点更接近原点N倍。我们猜想，这些是在Borel平面的领导奇点，他们是难以捉摸的重正子在弱耦合制度的化身。
Perturbation series in quantum field theory (QFT) are generally divergent asymptotic series which are also typically not Borel resummable in the sense that the resummed series is ambiguous. The ambiguity is associated with singularities in the Borel plane on the positive real axis. In quantum mechanics there are cases in which the ambiguity that arises in perturbation theory cancels against a similarly ambiguous contribution from instanton-anti-instanton events. In asymptotically free gauge theories, this mechanism does not suffice because perturbation theory develops ambiguities associated with singularities in the Borel plane which are closer to the origin by a factor of about N (the rank of the gauge group) compared to the singularities realized by instanton events. These are called IR renormalon poles, and on R^{4} they do not possess any known semiclassical realization. By using continuity on R(3) × S(1), and by generalizing the works of Bogomolny and Zinn-Justin to QFT, we identify saddle point field configurations, e.g., bion-antibion events, corresponding to singularities in the Borel plane which are of order N times closer to the origin than the four-dimensional instanton-anti-instanton singularities in the Borel plane. We conjecture that these are the leading singularities in the Borel plane and that they are the incarnation of the elusive renormalons in the weak coupling regime.