CANONICAL QUANTIZATION OF SPHERICALLY SYMMETRICAL GRAVITY IN ASHTEKAR SELF-DUAL REPRESENTATION

被引:136
作者
THIEMANN, T
KASTRUP, HA
机构
[1] Institut für Theoretische Physik, RWTH Aachen
关键词
D O I
10.1016/0550-3213(93)90623-W
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
We show that the quantization of spherically symmetric pure gravity can be carried out completely in the framework of Ashtekar's self-dual representation. Consistent operator orderings can be given for the constraint functionals yielding two kinds of solutions for the constraint equations, corresponding classically to globally nondegenerate or degenerate metrics. The physical state functionals can be determined by quadratures and the reduced hamiltonian system possesses two degrees of freedom, one of them corresponding to the classical Schwarzschild mass squared and the canonically conjugate one representing a measure for the deviation of the nonstatic field configurations from the static Schwarzschild one. There is a natural choice for the scalar product making the two fundamental observables self-adjoint. Finally, a unitary transformation is performed in order to calculate the triad-representation of the physical state functionals and to provide for a solution of the appropriately regularized Wheeler-DeWitt equation.
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页码:211 / 258
页数:48
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