Renormalization and renormalization group behaviour of the O(N) non-linear sigma-model in stochastic quantization

The renormalization and renormalization group behaviour of the two-dimensional O(N) non-linear sigma-model has been discussed in the framework of stochastic quantization. For this purpose the path integral representation of the generating functional of the extended stochastic correlation function for constrained systems has been given. The renormalization is formulated by use of the stochastic effective action which can be defined from this generating functional. The renormalization group behavior of the correlation function with different fictitious time arguments has also been investigated. It reduces to the normal one if all external fictitious times are taken to be equal.