{
  "id": "1606.05069",
  "version": "v1",
  "published": "2016-06-16T07:24:18.000Z",
  "updated": "2016-06-16T07:24:18.000Z",
  "title": "Misunderstanding that the Effective Action is Convex under Broken Symmetry",
  "authors": [
    "Nobu-Hiko Asanuma"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "hep-th",
    "quant-ph"
  ],
  "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 explicitly 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-16T07:24:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "effective action",
      "quantum field theory",
      "spontaneously broken symmetry",
      "zero field limit",
      "symmetry breaking necessarily accompanies non-convexity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}