The Poisson bracket { ⋅ ⋅ , ⋅ ⋅ } on (M, ω) is a bilinear operation on differentiable functions, defined by { f , g } = ω ω ( X f , X g ) ; the Poisson bracket of two functions on M is itself a function on M. The Poisson bracket is antisymmetric because: { f , g } = ω ω ( X f , X g ) = − − ω ω ( X g , X f ) = − − { g , f } .