标题： SO(2,1)共形异常：超越接触相互作用 显示英文标题

标题： SO(2,1) conformal anomaly: Beyond contact interactions

摘要： SO(2,1)对易子代数异常对称性破缺解的存在性被明确地扩展到了尺度不变接触相互作用的情况之外。 特别是，对于二维反平方势，膨胀和特殊共形电荷的守恒定律失效得到了展示。 因此，这种异常似乎是对称量子力学的一个普遍特征，而不仅仅是接触相互作用的产物。 此外，一个重整化过程将这种共形异常的出现追溯到理论的紫外区域，在该区域内存在明显的奇异性。 显示英文摘要

摘要： The existence of anomalous symmetry-breaking solutions of the SO(2,1) commutator algebra is explicitly extended beyond the case of scale-invariant contact interactions. In particular, the failure of the conservation laws of the dilation and special conformal charges is displayed for the two-dimensional inverse square potential. As a consequence, this anomaly appears to be a generic feature of conformal quantum mechanics and not merely an artifact of contact interactions. Moreover, a renormalization procedure traces the emergence of this conformal anomaly to the ultraviolet sector of the theory, within which lies the apparent singularity.