Secondly, G ( τ τ ) is (anti)periodic under shifts of β β . Because of the small domain within which the function is defined, this means just G ( τ τ − − β β ) = ζ ζ G ( τ τ ) , for 0 < τ τ < β β . Time ordering is crucial for this property, which can be proved straightforwardly, using the cyclicity of the trace operation.