Graded Poisson bracket
= Graded Poisson bracket
An even Poisson bracket on a space with commuting and anticommuting variables obeys $\{F,G\}=-(-1)^{|F||G|}\{G,F\}$ and the graded Leibniz rule. In particular the bracket of two odd functions is symmetric. Quantization turns the odd-odd bracket into an anticommutator.