六阶重力场action项度量变分的不可约形式和近似应力-能量张量
Irreducible forms for the metric variations of the action terms of sixth-order gravity and approximated stress-energy tensor
摘要：
我们提供了不可约的表达式的度量变化的引力作用量项构造从17个曲率不变量的阶数为6的导数的度量张量，即从几何项出现在对角热核或Gilkey-DeWitt系数$a_3$。然后，我们表示，对于一个四维时空，近似的应力-能量张量构造的重整化德威特-施温格有效作用量与一个大质量的标量场。我们还构造，为高维时空，无穷的反项的阶6的度量张量出现在爱因斯坦方程的左手边的导数，以及与立方Lovelock引力作用的贡献。在附录中，我们提供了一个我们所使用的几何关系的列表，这些几何关系对于四维背景下的双圈量子引力的计算或高维背景下的单圈量子引力的计算都是有帮助的。我们还得到了在四维背景中传播的大质量旋量场和大质量矢量场的近似应力-能量张量。
英文摘要：
We provide irreducible expressions for the metric variations of the gravitational action terms constructed from the 17 curvature invariants of order six in derivatives of the metric tensor i.e. from the geometrical terms appearing in the diagonal heat-kernel or Gilkey-DeWitt coefficient $a_3$. We then express, for a four dimensional spacetime, the approximated stress-energy tensor constructed from the renormalized DeWitt-Schwinger effective action associated with a massive scalar field. We also construct, for higher dimensional spacetimes, the infinite counterterms of order six in derivatives of the metric tensor appearing in the left hand side of Einstein equations as well as the contribution associated with the cubic Lovelock gravitational action. In an appendix, we provide a list of geometrical relations we have used and which are more generally helpful for calculations in two-loop quantum gravity in a four dimensional background or for calculations in one-loop quantum gravity in higher dimensional background. We also obtain the approximated stress-energy tensors associated with a massive spinor field and a massive vector field propagating in a four dimensional background.
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