Stochastic quantization of the nonlinear sigma model and the background field method (Q1330099)

The authors use the background field method for the study of the nonlinear \(\sigma\)-model on a Riemannian manifold in the context of stochastic quantization method. After presenting the functional-integral approach and extended stochastic correlation functions for scalar fields, they consider the background field generating functional and the stochastic quantization for the nonlinear \(\sigma\)-model. The generating functional for one-loop calculations is obtained by expanding the quantum part \(\psi^ i\) in powers of normal coordinates \(\xi^ i\) around a point, up to cubic powers.