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One 'standard' approach to quantization which always works is the path integral: $$\langle \mathcal O \rangle = \frac{\int [dQ dP] \mathcal O\exp \left( \int dx dt (\mathcal H + i P \dot Q)\right)}{\int [dQ dP] \exp \left( \int dx dt (\mathcal H + i P \dot Q)\right)}$$ where $\mathcal O$ is whatever operator you are interested in. ...