论文标题
在恒定侵蚀的riemannian和伪里曼尼亚语表面上的某些可延展系统的扩展哈米尔顿结构上
On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces
论文作者
论文摘要
我们证明了一个天然汉密尔顿家族的一家人家族的一般性和共同性，其中包括和概括了一些文献中最初定义在2d Minkowski空间中的文献。一些新的汉密尔顿人是Tremblay-Turbiner-Winternitz提出的欧几里得飞机上众所周知的可整合系统的完美类比，它们在Minkowski空间以及所有其他恒定曲率，Riemannian，Riemannian或Pseudo-Riemannian的2D歧管上进行了定义。我们还展示了耦合 - 恒定构型晶状体形态的应用如何使我们能够从先前的汉密尔顿获得新的可促进性汉密尔顿人。此外，对于Minkowski案例，我们显示了相应的量子汉密尔顿操作员的量子可共性。我们的结果是通过应用扩展的哈密顿系统理论获得的，这与扭曲的多种流形的几何形状有关。
We prove the integrability and superintegrability of a family of natural Hamiltonians which includes and generalises those studied in some literature, originally defined on the 2D Minkowski space. Some of the new Hamiltonians are a perfect analogy of the well-known superintegrable system on the Euclidean plane proposed by Tremblay-Turbiner-Winternitz and they are defined on Minkowski space, as well as on all other 2D manifolds of constant curvature, Riemannian or pseudo-Riemannian. We show also how the application of the coupling-constant-metamorphosis technique allows us to obtain new superintegrable Hamiltonians from the previous ones. Moreover, for the Minkowski case, we show the quantum superintegrability of the corresponding quantum Hamiltonian operator.Our results are obtained by applying the theory of extended Hamiltonian systems, which is strictly connected with the geometry of warped manifolds.
