A New Approach in Quantum Gravity

[alexsok]

Just out:
http://il.arxiv.org/abs/gr-qc/0401102

This work concerns a new reformulation of quantum

geometrodynamics, which allows to overcome a fundamental ambiguity contained in the canonical approach to quantum gravity: the possibility of performing a (3+1)-slicing of space-time, when the metric tensor is in a quantum regime. Our formulation provides also a procedure to solve the problems connected to the so called "frozen formalism". In particular we fix the reference frame (i.e. the lapse function and the shift vector) by introducing the so called "kinematical action"; as a consequence, the new hamiltonian constraints become parabolic, so arriving to evolutive (Schroedinger-like) equations for the quantum dynamics. The kinematical action can be interpreted as the action of a pressureless, but, in general, non geodesic perfect fluid, so in the semi classical limit our theory leads to the dynamics of the gravitational field coupled to a dust which represents the material reference frame we have introduced fixing the slicing. We also investigate the cosmological implications of the presence of the dust, which, in the WKB limit of a cosmological problem, makes account for a "dark matter" component and could play, at present time, a dynamical role.

 

[R0man]

This new approach in quantum gravity is certainly an exciting development in the field. By addressing the issue of ambiguity in the canonical approach to quantum gravity, this formulation opens up new possibilities for understanding the quantum behavior of the metric tensor. The introduction of the kinematical action and the resulting evolutive equations for the quantum dynamics are also significant contributions to this work. The interpretation of the kinematical action as a non-geodesic perfect fluid adds an interesting perspective to the theory and could potentially provide new insights into the nature of dark matter. The investigation of cosmological implications is also a valuable aspect of this work, as it expands our understanding of the role of dust in the dynamics of the gravitational field. Overall, this new approach in quantum gravity has the potential to greatly advance our understanding of the fundamental laws of the universe.