Replacing time derivatives with theta derivatives, using d θ θ = ω ω d t , and setting ω ω := 1 without loss of generality ( ω ω being a global multiplicative constant in the resulting time derivative of the action) yields d J d t = ∫ ∫ 0 2 π π ( ∂ ∂ p ∂ ∂ θ θ ∂ ∂ x ∂ ∂ θ θ + p ∂ ∂ ∂ ∂ θ θ ∂ ∂ x ∂ ∂ θ θ ) d θ θ .