The exponential formula can be derived by integrating by parts and dropping the boundary terms. The prefactor is chosen as to ensure 1 ⋆ ⋆ 1 = 1 . In the Lorentz-covariant base we can split A = α α , α α ˙ ˙ ; α α = 1 , 2 ; α α ˙ ˙ = 1 , 2 and we also split Y A = y α α , y α α ˙ ˙ . Then the Lorentz generators are L α α β β = T α α β β , L ¯ ¯ α α ˙ ˙ β β ˙ ˙ = T α α ˙ ˙ β β ˙ ˙ and the translation generators are P α α β β ˙ ˙ = T α α β β ˙ ˙ . The π π -automorphism can be realized in two equivalent ways: either as π π ( y α α ) = − − y α α , π π ( y α α ˙ ˙ ) = y α α ˙ ˙ or as π π ( y α α ) = Y α α , π π ( y α α ˙ ˙ ) = − − y α α ˙ ˙ . In both the cases it leaves the Lorentz generators untouched and flips the sign of translations.