Cortez, Jerónimo; Núñez, Dario; Quevedo, Hernando Gravitational fields and nonlinear \(\sigma\)-models. (English) Zbl 0977.83023 Int. J. Theor. Phys. 40, No. 1, 251-260 (2001). 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. Reviewer: Trandafir Balan (Craiova) Cited in 1 Document MSC: 83C45 Quantization of the gravitational field 81T10 Model quantum field theories Keywords:quantum field theory; nonlinear \(\sigma\)-models of gravitational field; Einstein-Rosen gravitational wave PDF BibTeX XML Cite \textit{J. Cortez} et al., Int. J. Theor. Phys. 40, No. 1, 251--260 (2001; Zbl 0977.83023) Full Text: DOI