Moyal bracket

In order to simplify the terms of order n > 3 we have to introduce the notion of the Moyal bracket. Given two symbols A(z hen) and B(z hes), corresponding to operators A and B, respectively, the Moyal bracket is defined as... 

We thus see that the computation of the symbol of the QNF operator is very similar to the classical case. The major difference is the use of the Moyal bracket in the quantum case which is more complicated than the Poisson bracket in the classical case. What remains to be done to get the Nth order QNF operator is to compute the Weyl quantization of the symbol H p(z fteff) ... 

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