标题： 非黎曼几何基础的引力理论中的局部尺度对称性和诺特定理电流的作用 显示英文标题

标题： Local scale symmetry in non-riemannian geometry based gravitational theories and the role of the noether current

摘要： 在本文中，我们深入探讨了局部尺度对称性以及相关诺特定律流在基于非黎曼背景空间的引力理论中的重要性。我们的重点是基于魏尔几何和黎曼-卡坦几何的引力理论。我们表明，当不存在超过无质量引力子的两个极化之外的新传播引力自由度时，局部尺度对称性与零诺特定律流相关。相反，在存在多于两个传播引力自由度的局部尺度不变理论中，局部尺度对称性与非零诺特定律流相关。已知结果表明魏尔对称性具有零诺特定律流，该结果被推广到非黎曼引力理论。例外情况是具有矢量非度规性的局部尺度不变引力理论，其中相关的诺特定律流是非零的。 显示英文摘要

摘要： In this paper, we delve into the significance of local scale symmetry and the role of the associated noether current, within gravitational theories which are based in non-riemannian background space. Our focus is in Weyl and in Riemann-Cartan geometry based gravitational theories. We show that local scale symmetry is associated with vanishing noether current whenever there are not new propagating gravitational degrees of freedom beyond the two polarizations of the massless graviton. In contrast, in local scale invariant theories where there are more than two propagating gravitational degrees of freedom, local scale symmetry is associated with nonvanishing noether current. The known result that Weyl symmetry has vanishing noether current, is generalized to non-riemannian gravitational theories. An exception are the local scale invariant gravitational theories with vectorial nonmetricity, where the associated noether current is nonvanishing.