Maxwell Construction for Scalar Field Theories with Spontaneous Symmetry Breaking
Maxwell Construction for Scalar Field Theories with Spontaneous Symmetry Breaking
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具有自发对称破缺的标量场论的麦克斯韦构造
DOI：
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发表时间：
2012
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通讯作者：
A. Tsapalis
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作者：
J. Alexandre;A. Tsapalis
本文对具有自发对称破缺特征的复杂标量模型的配分函数作了非微扰近似，明确地导出了在裸势极小值所限定的区域内的有效势的微扰性。这种衰减发生在无限体积的极限中，是支配配分函数的连续鞍点集求和的结果。证明了有效势的凸性，推广了O（N）对称标量理论的麦克斯韦构造.最后，我们讨论了为什么在阿贝尔Higgs理论中，有效势的衰减不能发生。1引言标量理论的有效势的凸性已经知道了很长时间[1]，并且是其在勒让德变换方面定义的结果[2]。在裸势具有自发对称破缺（SSB）的情况下，凸性是非微扰的，不能通过简单的环展开得到。作为两个非平凡鞍点竞争的结果，有效势在裸势的两个极小值之间变得不稳定[3]。通过类比货车的麦克斯韦结构
AbstractUsing anon-perturbative approximation forthe partitionfunction ofacomplex scalarmodel,which features spontaneous symmetry breaking, we explicitly derive the flattening of the effec-tive potential in the region limited by the minima of the bare potential. This flattening occursin the limit of infinite volume, and is a consequence of the summation over the continuousset of saddle points which dominate the partition function. We also prove the convexity ofthe effective potential and generalize the Maxwell Construction for scalar theories with O(N)symmetry. Finally, we discuss why the flattening of the effective potential cannot occur in theAbelian Higgs theory. 1 Introduction The convexity of the effective potential for a scalar theory has been known for a long time [1],and is a consequence of its definition in terms of a Legendre transform [2]. In the situationwhere the bare potential features spontaneous symmetry breaking (SSB), convexity is achievednon-perturbatively, and cannot be obtained by a naive loop expansion. The effective potentialbecomes flat between the two minima of the bare potential, as a consequence of the competitionof the two non-trivial saddle points [3]. By analogy with the Maxwell construction for a Van