标题： 洛伦兹不变性的自发破缺与诺姆-戈德斯通定理 显示英文标题

标题： Spontaneous Breakdown of the Lorentz Invariance and the Nambu-Goldstone Theorem

摘要： 在一个三维阿贝尔规范理论的课程中，洛伦兹不变性通过磁场所的动态生成而被自发打破。 一个原本拓扑质量光子变得无间隙，即在{\vec p}=0 时 p_0=0。 确实，光子是与洛伦兹不变性自发打破相关的尼尔-戈德斯通玻色子。 尽管由两个洛伦兹提升生成元产生的对称性被打破，似乎只出现了一个物理的尼尔-戈德斯通玻色子，即光子。 我们认为尼尔-戈德斯通定理中的瓦德恒等式由光子极点饱和。 显示英文摘要

摘要： In a class of three-dimensional abelian gauge theory the Lorentz invariance is spontaneously broken by dynamical generation of a magnetic field. An originally topologically massive photon becomes gapless, i.e. p_0=0 at {\vec p}=0. Indeed, the photon is the Nambu-Goldstone boson associated with the spontaneous breaking of the Lorentz invariance. Although symmetry generated by two Lorentz boost generators is broken, there seems to appear only one physical Nambu-Goldstone boson, namely a photon. We argue that the Ward identities in the Nambu-Goldstone theorem are saturated by the photon pole.