Non-perturbative and background-independent formulation of quantum gravity and its general problems

在复杂作用理论中，经过长时间的发展，我们提出了自动获得厄米哈密顿量的机制，并构建了一种新的支架形式，可以很好地处理复杂的坐标和动量。进一步，我们证明了在最终时间和初始时间之间的较大时间间隔内，未来包含理论中的对角元素几乎等于未来不包含理论中用修正内积定义的期望值。

In complex action theory we proposed the mechanism to automatically obtain a hermitian Hamiltonian after a long time development, and constructed a new bra-ket formalism, by which we can deal with complex coordinate and momentum properly. Furthermore, we showed that for a large time interval between the final and initial times a diagonal element in the future-included theory is almost equal to an expectation value in the future-not-included theory defined with a modified inner product.