Understand
We elaborate on the Ashtekar's formalism for spherically symmetric midisuperspaces and, for loop quantization, propound a new quantization scheme which yields a graph-preserving Hamiltonian constraint operator and by which one can impose the fundamental discreteness of loop quantum gravity a la the strategy of "improved" dynamics in loop quantum cosmology (LQC).
- Remarkable consequences are inferred at the heuristic level of effective dynamics: first, consistency of the constraint algebra regarding the Hamiltonian and diffeomorphism constraints fixes the improved quantization scheme to be of the form reminiscent of the improved scheme in LQC which preserves scaling invariance; second, consistency regarding two Hamiltonian constraints further demands the inclusion of higher order holonomy corrections and fixes a ratio factor of 2 for the improved scheme.
- It is suggested that the classical singularity is resolved and replaced by a quantum bounce which bridges a classical solution to another classical phase.
- However, the constraints violate briefly during the bouncing period, indicating that one cannot make sense of symmetry reduction by separating the degrees of freedom of the full theory into spherical and non-spherical ones in the vicinity of the quantum bounce, although the heuristic effective dynamics can still give a reliable semiclassical description of large-scale physics.