标题： 共形结构的畸变产生的隐藏对称性 显示英文标题

标题： Hidden symmetries from distortions of the conformal structure

摘要： 众所周知，在测地线运动的情况下，质量参数会破坏共形对称性。 当考虑非零测地线时，适当的共形Killing向量不再生成守恒荷。 我们研究引入质量实际上如何与共形领域中适当扭曲的出现相关，这些扭曲导致了新的守恒定律。 作为明显的例子，我们使用了一般的pp波度规，它最大限度地利用了这一特性。 我们研究了必要的几何条件，以便此类扭曲适用。 我们证明相对向量是变形变换的生成元，并证明它们与高阶（隐藏）对称性的联系。 除了pp波几何外，我们还以de Sitter度规的形式提供了一个额外的例子。 同样，适当的共形Killing向量可以被适当扭曲，以生成质量测地线的守恒量。 随后，我们引入了一个额外的对称性破缺效应。 后者通过考虑一种Bogoslovsky类型的线元来实现，该线元涉及一个破坏洛伦兹对称的参数。 我们再次以pp波情况为指导，研究被破坏的对称性——这次也与Killing向量有关——是如何被原始生成元的扭曲所替代的。 我们进一步分析和讨论导致这些扭曲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.