A choice of gauge in general relativity is well-known to have a twofold aim: to render dynamics unique (as in any gauge theory), and to define spacetime points. A coherent description of both aspects of gauge in canonical theory is achieved extending some ideas by Kuchavr. Quantum theory is gauge invariant, if the definition of spacetime points is not changed by the transformations. The apparatus is applied to a model: spherically symmetric gravitating shell. Calculations are completed for two gauges that disagree on points definition. Unitarily inequivalent quantum theories result. For example, the position of the horizon formed by shell collapse is fuzzy in one, but sharp in the other gauge. In general, gauge invariance of observable properties is unlikely to extend from classical to quantum theory if the quantization method employs the concept of spacetime. This motivates spacetime-free descriptions of dynamics in quantum gravity.
19th Texas Symposium on Relativistic Astrophysics and Cosmology
- Pub Date:
- December 1998