Quantization of ideal fluids: Perturbative or non-perturbative approach

Perturbative and non-perturbative types of approaches to quantization of ideal fluid flows are considered and compared. The results on stability of particular vortex structures obtained in the framework of the standard energy-Casimir method are reminded for the purpose of checking connection between stability and quantizability. Results on geometric quantizability derived by Goldin, Menikoff and Sharp for these structures are also reminded. The discrepancy between results of these two approaches being an evidence for non-perturbative character of quantization of ideal fluids is stressed. New non-perturbative approach exploiting ideas from Ashtekar programme of quantization of gravity is formulated. Some applications of the new approach in description of superfluid helium are briefly shown.