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Gravitational fields and nonlinear $$\sigma$$-models. (English) Zbl 0977.83023
The authors’ abstract: It is shown that different types of gravitational fields can be analyzed as nonlinear $$\sigma$$-models. We show that the Einstein-Hilbert action for stationary axisymmetric fields, Einstein-Rosen gravitational wave, and Gowdy cosmological models can be expressed in terms of a Lagrangian density for the SL$$(2,\mathbb{R})/SO(2)$$ $$\sigma$$-model. We discuss the possibility of using these results to quantize gravitational fields.

##### MSC:
 83C45 Quantization of the gravitational field 81T10 Model quantum field theories
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