关于广义相对论的Brown-York与Quadratic Spinor作用量

广义相对论希尔伯特作用量在类空无穷远发散．如果要在类空无穷远得到收敛，则需要在希尔伯特作用量加上边界修正项．比较在类空无穷远收敛的Brown—York作用量，以及二次方旋量场（Quadratic Spinor）作用量．发现当狄拉克（Dirac）旋量场在边界超曲面上满足Witten方程时，二次方旋量场作用量在渐进类空无穷远等于Brown—York作用量．

On Brown-York and Quadratic Spinor actions of general relativity

In the asymptotically spatial infinity, the Hilbert action diverges. In order to obtain a finite action, it is necessary to adjust by a boundary term. We compare two such actions, one is the Brown-York action, and the other is the Quadratic Spinor action. We found that, at asymptotically spatial infinity, when the spinors at boundary hypersurface satisfy the Witten equations, the Quadratic Spinor action reduced to the Brown-York action.