Titlebook: Probabilistic Methods in Quantum Field Theory and Quantum Gravity; P. H. Damgaard,H. Hüffel,A. Rosenblum Book 1990 Springer Science+Busine

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Solved and Unsolved Problems in the Stochastic Quantization of Gravityres a generally covariant version of stochastic quantization for its remedy. These necessary generalizations of the original Parisi-Wu formalism are the main topics of this review. We shall see at the end that, perturbatively, the solution of problem two even provides another solution to problem one.

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Slave Equations for Connected Correlation Functionshat the error analysis is straightforward because the signal is computed directly as the mean of an unbiassed estimator. The second advantage is the subject of this talk. It can be shown that the error on G(t) . with increasing t and that this decrease is . in theories with a mass gap.

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Quantization = Geometry + Probabilityhoices. Natural extensions of this geometric-probabilistic quantization procedure to the case of fields yield proposals for (i) a quantization scheme for a scalar field in an arbitrary background metric, and (ii) a quantization scheme for the gravitational field fully respecting the positivity of the three metric.

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The O (N)-Symmetric Non-Linear σ-Model to Three Leading Orders in 1/Nruncations, we find systematic errors which are smaller than the expected magnitude of neglected terms, both for the mass gap and for the susceptibility. This result is uniform in the inverse coupling β, and valid for . as small as 3. We conclude that the 1/.-series approach the exact results as rapidly as one could ever hope for.

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