Multiscale renormalization group methods for effective potentials with multiple scalar fields
Multiscale renormalization group methods for effective potentials with multiple scalar fields
复制标题
多标量场有效势的多尺度重整化群方法
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
D. McKeon
中科院分区：
文献类型：
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作者：
T. Steele;Zhi;D. McKeon
本文综述了多尺度重整化群（RG）方法，并将其应用于多标量场辐射对称性破缺的有效势分析，从而将Gildener &温伯格（GW）方法推广到弱耦合极限之外。用一个包含两个相互作用的真实的标量场的模型来说明多尺度RG方法，并计算了该模型的多尺度RG函数，使其达到单圈阶。η $函数和双圈阶的反常质量维数。通过引入一个额外的重整化标度，可以将模型中的有效势映射到一个具有O（2）对称结构的RG等价形式上，沿着多重整化标度空间中的一个特定轨迹，从而得到一个简化形式的有效势。它表明，在原始模型中的有效势的物理内容，参考一个单一的传统重整化尺度，可以从一个特定的RG-轨迹，连接到这个多尺度O（2）对称形式的有效势提取。这些多尺度方法在包含$O（M）的多标量模型中的有效势的推广 本文还讨论了对称性O（N）$.
Multi-scale renormalization group (RG) methods are reviewed and applied to the analysis of the effective potential for radiative symmetry breaking with multiple scalar fields, allowing an extension of the Gildener & Weinberg (GW) method beyond the weak coupling limit. A model containing two interacting real scalar fields is used to illustrate multi-scale RG methods and the multi-scale RG functions of this model are calculated to one-loop order for the $eta$ function and two-loop order for the anomalous mass dimension. The introduction of an extra renormalization scale allows the mapping of the effective potential in this model onto an RG-equivalent form with an O(2) symmetric structure along a particular trajectory in the multiple renormalization-scale space, leading to a simplified form of the effective potential. It is demonstrated that the physical content of the effective potential in the original model, referenced to a single conventional renormalization scale, can be extracted from a particular RG-trajectory that connects to this multi-scale O(2)-symmetric form of the effective potential. Extensions of these multi-scale methods for effective potentials in models containing multiple scalars with $O(M) imes O(N)$ symmetry are also discussed.