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• W2095242592 abstract "Abstract We apply stochastic quantization to two-dimensional gravity. The Laplace operator acting on the space of all metrics takes a particularly simple form in terms of the Beltrami parametrization. We show the equivalence between the quantum theory defined by the standard Faddeev-Popov gauge fixing of the two-dimensional diffeomorphism invariance and the one defined by stochastic quantization. We do so by using the gauge freedom left in the Langevin equation of a diffeomorphism-invariant theory to adjust the drift force. Another choice of the drift force, comparable to that of Zwanziger for Yang-Mills theories, seems to avoid the analogue of the Gribov ambiguity, i.e. the necessity of the by-hand restriction to one fundamental domain. We relate the two-dimensional gravity to a three-dimensional theory, based on the three-dimensional gravitational Chern-Simons action for SL(2, C ), ISO(3) or SU(2) × SU(2) (depending on the genus of the two-dimensional Riemann surface), in which all fields of the stochastic quantization have been distributed as components of the gauge fields. To study the three-dimensional theory, stochastic quantization can be applied once more. This gives a theory with the action of topological gravity in four dimensions, namely the Pontrjagin invariant ∫ N 2 × R × R tr R ∧ R , gauge fixed by self-duality conditions." @default.
• W2095242592 created "2016-06-24" @default.
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• W2095242592 date "1990-12-01" @default.
• W2095242592 modified "2023-09-26" @default.
• W2095242592 title "Stochastic quantization of 2D gravity and its link with 3D gravity and topological 4D gravity" @default.
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• W2095242592 doi "https://doi.org/10.1016/0550-3213(90)90290-t" @default.
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