QUANTUM GRAVITY OF A BRANE-LIKE UNIVERSE

摘要: Quantum gravity of a brane-like Universe is formulated, and its Einstein limit approached. Regge–Teitelboim embedding Arnowitt–Deser–Misner formalism, parametrized by the coordinates yA(t,xi), governed some ρAB(y,y′,y″). Invoking novel Lagrange multiplier λ, accompanying lapse function N shift vector Ni, we derive quadratic Hamiltonian The inclusion mattter resembles minimal coupling. Setting PA=-i(δ/δyA), bifurcated Wheeler–Dewitt-like equation. gravity, associated with λ being certain fourfold degenerate eigenvalue ρAB, characterized vanishing center-of-mass momentum ∫PAd3x=0. Troublesome (ρ-λI)-1 then replaced regular M-1, such that M-1(ρ-λI) defines projection operator, modifying accordingly.