New Asymptotic Expanstion Method for the Wheeler-DeWitt Equation

Details New Asymptotic Expanstion Method for the Wheeler-DeWitt Equation New Asymptotic Expanstion Method for the Wheeler-DeWitt Equation

1995-11-13

arxiv.org/abs/gr-qc/9511038v1

Phys.Rev.D52:3382-3391,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages of Latex file, revtex

Scientific paper

10.1103/PhysRevD.52.3382

A new asymptotic expansion method is developed to separate the Wheeler-DeWitt equation into the time-dependent Schr\"{o}dinger equation for a matter field and the Einstein-Hamilton-Jacobi equation for the gravitational field including the quantum back-reaction of the matter field. In particular, the nonadiabatic basis of the generalized invariant for the matter field Hamiltonian separates the Wheeler-DeWitt equation completely in the asymptotic limit of $m_p^2$ approaching infinity. The higher order quantum corrections of the gravity to the matter field are found. The new asymptotic expansion method is valid throughout all regions of superspace compared with other expansion methods with a certain limited region of validity. We apply the new asymptotic expansion method to the minimal FRW universe.

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