## Abstract

Quantum gravity of a brane-like Universe is formulated, and its Einstein limit is approached. Regge-Teitelboim embedding of Arnowitt-Deser-Misner formalism, parametrized by the coordinates y^{A} (t, x^{i}), is governed by some ρ_{AB}(y, y′, y″). Invoking a novel Lagrange multiplier λ, accompanying the lapse function N and the shift vector N^{i}, we derive the quadratic Hamiltonian script H sign = 1/2 N [P_{A}((ρ - λI)^{-1})^{AB} P_{B} + λ] + N^{i}y,^{A}_{i}P_{A}. The inclusion of matter resembles minimal coupling. Setting P_{A} = -i(δ/δy^{A}), we derive a bifurcated Wheeler-Dewitt-like equation. Einstein gravity, associated with λ being a certain fourfold degenerate eigenvalue of ρ_{AB}, is characterized by a vanishing center-of-mass momentum ∫ P_{A} d^{3}x = 0. Troublesome (ρ - λI)^{-1} is then replaced by regular M^{-1}, such that M^{-1} (ρ - λI) defines a projection operator, modifying the Hamiltonian accordingly.

Original language | English |
---|---|

Pages (from-to) | 2187-2192 |

Number of pages | 6 |

Journal | Modern Physics Letters A |

Volume | 13 |

Issue number | 27 |

DOIs | |

State | Published - 7 Sep 1998 |

## ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Astronomy and Astrophysics
- General Physics and Astronomy