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        "quote": "此时真空不是 $\\widehat N$ 的本征态，没有确定的粒子数。若 $[\\widehat N,\\widehat H]=0$，则 $|\\theta\\rangle$ 都具有与 $|0\\rangle$ 相同的能量，形成由 $\\theta$ 标记的不同真空。此时称 $U(1)$ 发生[<u class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/spontaneous-symmetry-breaking\" data-concept-identity=\"urn:uuid:ca209073-6b0b-4faa-b78f-0d00d3d11d24\" data-concept-route=\"/concept-identities#concept-ca209073-6b0b-4faa-b78f-0d00d3d11d24\" id=\"first-604a9d7ff08d53f734ab-zh\">自发对称破缺(spontaneous symmetry breaking)</u>](../../../../../concepts/quantum-mechanics/spontaneous-symmetry-breaking)。在超导体的非相对论场论描述中，电子配对降低能量并凝聚到最低能量态，该态没有确定的粒子数。",
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        "quote": "The vacuum is not an eigenstate of $\\widehat N$ and has no definite particle number. If $[\\widehat N,\\widehat H]=0$, all $|\\theta\\rangle$ have the same energy. This vacuum degeneracy with non-invariant vacua is “[<u class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/spontaneous-symmetry-breaking\" data-concept-identity=\"urn:uuid:ca209073-6b0b-4faa-b78f-0d00d3d11d24\" data-concept-route=\"/concept-identities#concept-ca209073-6b0b-4faa-b78f-0d00d3d11d24\" id=\"first-604a9d7ff08d53f734ab-en\">spontaneous symmetry breaking</u>](../../../../../concepts/quantum-mechanics/spontaneous-symmetry-breaking)” of $U(1)$. In superconductivity, electrons pair in an energetically favorable way, condensing into a ground state without definite particle number.",
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