标题： 边缘的尺度不变性 显示英文标题

标题： Scale Invariance at the Edge

摘要： 讨论了生活在三维时空及其平坦余维数为一的边界上的费米子理论的一些方面，特别是边界条件保留标度和平移不变性但破坏剩余洛伦兹和共形对称性的案例。 这个案例很有趣，因为狄拉克方程具有归一化的稳定边缘态，在量子化过程中必须考虑这些态。 我们证明了边缘态对狄拉克场量子化的一个后果是，即使标度、C和P对称性是理论的良好对称性，狄拉克场论中也不存在同时满足这些对称性的状态。 狄拉克场的标度不变态要么包含非零的标度协变动量密度，要么包含集中在边缘附近的U(1)电荷密度。 显示英文摘要

摘要： Some aspects of the theory of fermions living on three dimensional spacetime with a flat co-dimension one boundary are discussed, particularly a case where the boundary condition preserves scale and translation invariance but violates the residual Lorentz and conformal symmetries. This case is interesting because the Dirac equation has normalizable stationary edge states which must be taken into account in the quantization. We show that a consequence of the edge states for quantization of the Dirac field is that there are no states of the Dirac field theory which are simultaneously scale, C and P invariant even when these are good symmetries of the theory. The scale invariant states of the Dirac field contain either a nonzero scale covariant momentum density or a U(1) charge density concentrated near the edge.