Misunderstanding that the Effective Action is Convex under Broken Symmetry

Nobu-Hiko Asanuma

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arXiv · 1606.05069

Misunderstanding that the Effective Action is Convex under Broken Symmetry

Nobu-Hiko Asanuma

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Abstract

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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BibTeX RIS

Nobu-Hiko Asanuma. 2016-06-16. Misunderstanding that the Effective Action is Convex under Broken Symmetry. https://arxiv.org/abs/1606.05069

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