Note: If one adopts the convention { ( + , − − , − − , − − ) ; l a n a = 1 , m a m ¯ ¯ a = − − 1 } , the definitions of Ψ Ψ i should take the opposite values; that is to say, Ψ Ψ i ↦ ↦ − − Ψ Ψ i after the signature transition.