We discuss spontaneously broken quantum field theories with a continuous global symmetry group via the constraint effective potential. Employing lattice simulations with constrained values of the order parameter, we demonstrate explicitly that the path integral is dominated by inhomogeneous field configurations and that these are unambiguously related to the flatness of the effective potential in the broken phase. We determine characteristic features of these inhomogeneities, including their topology and the scaling of the associated excess energy with their size. Concerning the latter we introduce the differential surface tension—the generalization of the concept of a surface tension pertaining to discrete symmetries. Within our approach, spontaneous symmetry breaking is captured merely via the existence of inhomogeneities, i.e., without the inclusion of an explicit breaking parameter and a careful double limiting procedure to define the order parameter. While here we consider the three-dimensional O(2) model, we also elaborate on possible implications of our findings for the chiral limit of QCD.

中文翻译：

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通过不均匀性和微分表面张力自发破坏对称性

我们通过约束有效势讨论具有连续全局对称群的自发破缺量子场论。采用具有有序参数约束值的晶格模拟，我们明确地证明了路径积分由非均匀场配置主导，并且这些与破碎相中有效势的平坦度明确相关。我们确定了这些不均匀性的特征，包括它们的拓扑结构和相关过剩能量与其尺寸的缩放比例。关于后者，我们引入了微分表面张力——与离散对称性有关的表面张力概念的概括。在我们的方法中，自发对称性破缺仅通过不均匀性的存在来捕获，即，没有包含明确的破坏参数和仔细的双重限制程序来定义顺序参数。虽然在这里我们考虑三维 O(2) 模型，但我们还详细说明了我们的发现对 QCD 手性极限的可能影响。