标题： 度规表示下量子引力的约束与解 显示英文标题

标题： Constraints and Solutions of Quantum Gravity in Metric Representation

摘要： 我们构造正则化的惠勒-德维特算符，要求量子引力的约束代数无反常。我们发现，对于某些波函数子集，这些波函数是数量密度的积分，可以满足这一条件。我们进一步寻找量子引力的精确解，这些解的形式为紧致三维流形体积和平均曲率的泛函。 显示英文摘要

摘要： We construct the regularised Wheeler-De Witt operator demanding that the algebra of constraints of quantum gravity is anomaly free. We find that for a subset of all wavefunctions being integrals of scalar densities this condition can be satisfied. We proceed to finding exact solutions of quantum gravity being of the form of functionals of volume and average curvature of compact three-manifold.