标题： 诺特对称性在牛顿力学和宇宙学中的应用 显示英文标题

标题： Noether Symmetry in Newtonian Dynamics and Cosmology

摘要： 分析了一种新的牛顿动力学对称性，这对应于转换到加速参考系，这会将恒定的引力场引入系统中。 我们考虑向引力势\(\phi \)添加一个线性贡献，该贡献可用于抵消由于转换到加速参考系而产生的引力场，这两个操作的结合随后产生一种对称性。 这种对称性导致了一个守恒的诺特流。 在特殊情况下分析了守恒电荷。 如果诺特流在无限远处产生通量，则电荷可能不守恒，但对于孤立系统，可以通过转换到质心（CM）系来消除这种通量。 在质心系中，诺特电荷为零。然后我们研究了宇宙学原理与通过此类对称性（Benisty和Guendelman在Mod Phys Lett A 35:2050131, 2020中提出）表述的牛顿动力学之间的联系，但没有采用作用量形式。 对于宇宙学相关的坐标系的均匀行为导致零诺特流，在这种情况下要求牛顿势在对称性下不变，从而得到弗里德曼方程，这些方程作为对称性的相容条件出现。 显示英文摘要

摘要： A new symmetry for Newtonian Dynamics is analyzed, this corresponds to going to an accelerated frame, which introduces a constant gravitational field into the system and subsequently. We consider the addition of a linear contribution to the gravitational potential \(\phi \) which can be used to cancel the gravitational field induced by going to the accelerated from, the combination of these two operations produces then a symmetry. This symmetry leads then to a Noether current which is conserved. The conserved charges are analyzed in special cases. The charges may not be conserved if the Noether current produces flux at infinity, but such flux can be eliminated by going to the CM (center of mass) system in the case of an isolated system. In the CM frame the Noether charge vanishes, Then we study connection between the Cosmological Principle and the Newtonian Dynamics which was formulated via a symmetry (Benisty and Guendelman in Mod Phys Lett A 35:2050131, 2020) of this type, but without an action formulation. Homogeneous behavior for the coordinate system relevant to cosmology leads to a zero Noether current and the requirement of the Newtonian potential to be invariant under the symmetry in this case yields the Friedmann equations, which appear as a consistency condition for the symmetry.