论文标题
Lorentzian光谱Zeta在渐近的Minkowski空间上发挥作用
Lorentzian spectral zeta functions on asymptotically Minkowski spacetimes
论文作者
论文摘要
在本说明中，我们考虑了Minkowski空间的扰动以及Wave Operator $ \ square_g $的更一般的空位本质上是自我偶数。我们回顾了一个最近的结果，该结果给出了洛伦兹光谱Zeta功能密度的均方根延续，即复杂功率的痕量密度$α\ mapsto（\ square_g-i \ varepsilon）^{ - α} $。在均匀的$ n \ geq 4 $中，在$ \ frac {n} {2} -1 $中的残留物显示为标量曲率的倍数，在限制$ \ varepsilon \ to 0^+$中。这产生了洛伦兹签名重力的光谱作用。
In this note, we consider perturbations of Minkowski space as well as more general spacetimes on which the wave operator $\square_g$ is essentially self-adjoint. We review a recent result which gives the meromorphic continuation of the Lorentzian spectral zeta function density, i.e. of the trace density of complex powers $α\mapsto (\square_g-i \varepsilon)^{-α}$. In even dimension $n\geq 4$, the residue at $\frac{n}{2}-1$ is shown to be a multiple of the scalar curvature in the limit $\varepsilon\to 0^+$. This yields a spectral action for gravity in Lorentzian signature.
