自相互作用相对论性 Luttinger 费米子的平均场理论
Mean-field theory for self-interacting relativistic Luttinger fermions
AI总结：
本文研究具有局部自相互作用的相对论性 Luttinger 费米子量子场论，利用大味数极限下精确的平均场理论，发现两个模型通过量纲嬗变将渐近自由高能区与含真空凝聚的有序低能相联系，并分析了传播子解析结构。
摘要：
我们研究一类具有相对论性 Luttinger 费米子及标量通道局部自相互作用的量子场论。为理解可能的低能相，我们首先对源自标量费米子双线性的质量项集合进行了分类。对于大味数情形，我们证明每个模型均存在一个使理论渐近自由的耦合分支。为探讨长程行为，我们采用在大味数极限下精确的平均场理论。我们确定了两个发生量纲嬗变的模型，它们将渐近自由的高能区与维持真空凝聚的有序低能相互联。我们还研究了 Luttinger 费米子传播子在各种可能能隙相中的解析结构。
英文摘要：
We investigate a class of quantum field theories with relativistic Luttinger fermions and local self-interaction in scalar channels. For an understanding of possible low-energy phases, we first classify the set of mass terms arising from scalar fermion bilinears. For large flavor numbers, we show that each of our models features a coupling branch in which the theory is asymptotically free. In order to address the long-range behavior, we use mean-field theory which is exact in the limit of large flavor numbers. We identify two models which undergo dimensional transmutation, interconnecting the asymptotically free high-energy regime with an ordered low-energy phase sustaining a vacuum condensate. We also study the analytic structure of the Luttinger-fermionic propagator in the various possible gapped phases.
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