标题： 从共形结构的扭曲中产生的隐藏对称性 显示英文标题

标题： Hidden symmetries from distortions of the conformal structure

摘要： 人们早已明确，质量参数在测地线运动的情况下会破坏共形对称性。 当考虑非零测地线时，适当的共形Killing矢量将不再生成守恒荷。 我们研究了质量的引入实际上是如何与共形部分中适当畸变的出现相关联的，这些畸变导致新的守恒定律的产生。 作为一个显著的例子，我们使用了一般的pp波度规，该度规充分利用了这一性质。 我们研究了必要的几何条件，使得这种类型的畸变可以应用。 我们证明相关的矢量是不等构变换的生成元，并证明了它们与高阶（隐藏）对称性的联系。 除了pp波几何之外，我们还提供了另一个例子，即de Sitter度规。 同样，适当的共形Killing矢量可以被畸变以生成具有质量的测地线的守恒量。 随后，我们通过引入另一种对称破缺效应继续研究。 后者通过对考虑Bogoslovsky型线元来实现，其中涉及洛伦兹破缺参数。 我们再一次利用pp波情况作为指导来研究如何用原始生成元的畸变来替代被破缺的对称性——这次这些对称性也与Killing矢量有关。 我们进一步分析和讨论了导致这些畸变出现的必要几何条件。 显示英文摘要

摘要： It is well established that the mass parameter breaks the conformal symmetries in the case of geodesic motion. The proper conformal Killing vectors cease to generate conserved charges when non-null geodesics are considered. We examine how the introduction of the mass is actually related to the appearance of appropriate distortions in the conformal sector, which lead to new conservation laws. As a prominent example we use a general pp-wave metric, which exploits this property to the maximum. We study the necessary geometric conditions, so that such types of distortions are applicable. We show that the relative vectors are generators of disformal transformations and prove their connection to higher order (hidden) symmetries. Except from the pp-wave geometry, we also provide an additional example in the form of the de Sitter metric. Again, the proper conformal Killing vectors can be appropriately distorted to generate conserved quantities for massive geodesics. Subsequently, we proceed by introducing an additional symmetry breaking effect. The latter is realized by considering a Bogoslovsky type of line-element, which involves a Lorentz violating parameter. We utilize once more the pp-wave case as a guide to study how the broken symmetries - this time also related to Killing vectors - are substituted by distortions of the original generators. We further analyze and discuss the necessary geometric conditions that lead to the emergence of these distortions.