时空度规共形修正的Hamilton映射：Kaluza-Klein和TeVeS
Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS
摘要：
已经证明，一类非相对论性哈密顿系统的运动轨道可以描述为流形上的测地线流和相应的对偶。这种方法可以应用于与相对论系统相关联的时空中的四维轨道流形。我们证明了一个产生爱因斯坦测地线的相对论性哈密顿量，加上一个世界标量场，可以与另一个具有共形修正度规的哈密顿量相对应。这样的构造可以解释贝肯斯坦在后牛顿极限下实现米尔格罗姆MOND理论的部分要求。通过这种对应关系，银河系旋转曲线对MOND理论的约束就意味着对世界标量场结构的约束。然后，我们使用的事实是，一个哈密顿量与矢量规范场的结果，通过这样的共形映射，在卡鲁扎-克莱因型理论，并指出如何TeVeS结构的贝肯斯坦和桑德斯可以放在这个框架。本文给出了规范场${\cal U}_μ$上一类保持Bekenstein-Sanders条件${\cal U}_μ{\cal U}^μ= -1$的无穷小规范变换.产生这些规范场的基本量子结构是希尔伯特丛，并且规范变换引起场的非对易行为，即，他们变成了杨米尔斯型工作在无穷小规范邻域的初始阿贝尔理论，我们表明，在阿贝尔极限的杨米尔斯场方程提供的非线性项，可以避免焦散奇异发现的Contaldi，等人。
英文摘要：
It has been shown that the orbits of motion for a wide class of nonrelativistic Hamiltonian systems can be described as geodesic flows on a manifold and an associated dual. This method can be applied to a four dimensional manifold of orbits in spacetime associated with a relativistic system. We show that a relativistic Hamiltonian which generates Einstein geodesics, with the addition of a world scalar field, can be put into correspondence with another Hamiltonian with conformally modified metric. Such a construction could account for part of the requirements of Bekenstein for achieving the MOND theory of Milgrom in the post-Newtonian limit. The constraints on the MOND theory imposed by the galactic rotation curves, through this correspondence, would then imply constraints on the structure of the world scalar field. We then use the fact that a Hamiltonian with vector gauge fields results, through such a conformal map, in a Kaluza-Klein type theory, and indicate how the TeVeS structure of Bekenstein and Sanders can be put into this framework. We exhibit a class of infinitesimal gauge transformations on the gauge fields ${\cal U}_μ$ which preserve the Bekenstein-Sanders condition ${\cal U}_μ{\cal U}^μ= -1$. The underlying quantum structure giving rise to these gauge fields is a Hilbert bundle, and the gauge transformations induce a non-commutative behavior to the fields, i.e., they become of Yang-Mills type. Working in the infinitesimal gauge neighborhood of the initial Abelian theory, we show that in the Abelian limit the Yang-Mills field equations provide nonlinear terms which may avoid the caustic singularity found by Contaldi, et al.
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