关于有效Action在对称性破缺下是凸的误解
Misunderstanding that the Effective Action is Convex under Broken Symmetry
摘要：
普遍认为有效作用量是凸的，并有一个平底下破缺的整体对称性被证明是错误的。我们表明，在量子场论的有效作用量或统计力学的自由能中，自发对称性破缺必然伴随着非凸性，并阐明了非凸性的大小。对于量子场论，也证明了当系统处于非凸区域时，平移不变性自发破缺，并且对称性自发破缺的不同真空不能叠加。作为非凸性的应用，我们研究了在自发破缺对称性的零场极限下的一级相变，并提出了一个简单的服从玻恩规则的相共存模型.
英文摘要：
The widespread belief that the effective action is convex and has a flat bottom under broken global symmetry is shown to be wrong. We show spontaneous symmetry breaking necessarily accompanies non-convexity in the effective action for quantum field theory, or in the free energy for statistical mechanics, and clarify the magnitude of non-convexity. For quantum field theory, it is also proved that translational invariance breaks spontaneously when the system is in the non-convex region, and that different vacua of spontaneously broken symmetry cannot be superposed. As applications of non-convexity, we study the first-order phase transition which happens at the zero field limit of spontaneously broken symmetry, and we propose a simple model of phase coexistence which obeys the Born rule.
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