Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-06-20
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
18 pages, no figures
Scientific paper
We present a novel solution of the Wheeler--DeWitt equation based on the model resulting due to application of the generalized one-dimensional (1D) conjecture. The conjecture extends the global 1D one on wave functions dependent on both matter fields and a generalized dimension which is a functional of the global one. The residual singularity in the effective potential is eliminating by an appropriate choice of the dimension. Application of the dimensional reduction within the obtained two-component 1D model yields the Dirac equation which is solved in an exact way. By use of the inverted change of variables in this solution we construct a general solution.
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