The above inequality is saturated by the solution of d x d τ τ = 2 V ( x ) with the condition x ( τ τ a ) = − − 1 and x ( τ τ b ) = 1 . Such solutions exist, and the solution takes the simple form when τ τ a = − − ∞ ∞ and τ τ b = ∞ ∞ . The explicit formula for the instanton solution is given by