Wheeler-DeWitt Equation and Bondi-Metzner-Sachs (BMS) Symmetry

The Hamiltonian formulation of the BMS symmetry on spacelike hypersurfaces enables one to define its action on solutions of the Wheeler-DeWitt equation. Using the Becchi-Rouet-Stora-Tyutin (BRST) reformulation of the theory, we provide operator expressions for the matrix elements of the BMS operators between Wheeler-DeWitt states. To that end, we construct the BRST-invariant extensions of the BMS generators, which form a BRST extension of the BMS algebra.