Basis states for gravitons in non-perturbative loop representation space
arXiv:gr-qc/9807013
Abstract
A relation between the non-perturbative loop representation space and the semi-classical loop representation space is studied. A sector of (approximate) states and a sector of operators in the non-perturbative loop representation space are made related respectively to the physical states and the basic variables of the semi-classical loop representation space through a transformation. This transformation makes a construction of graviton states within the non-perturbative theory possible although the notion of gravitons originally emerged from semi-classical perturbative treatments. This transformation is ``exact'' in the sense that it does not contain an error term, a fact contrast to the previous construction of a similar transformation. This fact allows the interpretation that these graviton states represent free gravitons even after introducing the self-interaction of gravitons into the theory; the presence of an error term of order of possible perturbative self-interaction would spoil this interpretation. The existence of such an ``exact'' relation of the two theories supports the potential ability of the non-perturbative loop representation quantum gravity to address the physics of gravitons, namely quanta for large scale small fluctuations of gravitational field in the flat background spacetime.
Latex, 21 pages, No figure
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