The leading quantum part, neglecting the higher order product of derivatives in the residual expression, is then equal to ∑ ∑ r ′ ( d B d J [ r ′ ] ( k − − r ′ ) A [ r ′ , k ] − − d A d J [ k − − r ′ ] r ′ B [ 0 , r ′ ] ) so that, finally, ( A B − − B A ) [ 0 , k ] = ∑ ∑ r ′ ( d B d J [ r ′ ] i d A d θ θ [ k − − r ′ ] − − d A d J [ k − − r ′ ] i d B d θ θ [ r ′ ] ) which can be identified with i times the k th classical Fourier component of the Poisson bracket.