General relativity has the property that, under the natural projection mapping, the image of the constraint surface in the phase space is a proper subset of the configuration space. This feature is not shared by other field theories of direct physical interest such as the Yang-Mills theory, nor by constrained systems which have been modeled after general relativity and analyzed in detail. Therefore, to gain insight into this feature, a new example with a finite number of degrees of freedom is introduced and quantized. The analysis suggests that, in the canonical approach, the reduced phase-space method is likely to yield an incomplete description of quantum gravity. In particular, contrary to the indication provided by this method, quantum gravity may admit states with negative energies.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)