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Dynamical content of quantum diffeomorphisms in two-dimensional quantum gravity

V. Aldaya·J. L. Jaramillo
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Abstract

A model for 2D-quantum gravity from the Virasoro symmetry is studied. The notion of space-time naturally arises as a homogeneous space associated with the kinematical (non-dynamical) SL(2,R) symmetry in the kernel of the Lie-algebra central extension for the critical values of the conformal anomaly. The rest of the generators in the group, L_n (n>1, n<-1), mix space-times with different constant curvature. Only in the classical limit all space-times can be identified, defining a unique Minkowski space-time, and the operators L_n (n<1, n<-1) gauged away. This process entails a restriction to SL(2,R) subrepresentations, which creates a non-trivial two-dimensional symplectic classical phase space. The present model thus suggests that the role of general covariance in quantum gravity is different from that played in the classical limit.

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V. Aldaya, J. L. Jaramillo. 2000-03-24. Dynamical content of quantum diffeomorphisms in two-dimensional quantum gravity. https://doi.org/10.1016/s0920-5632(00)00773-8

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