The metric of choice is given by η = diag(−1, 1, 1, 1), and the physics convention for Lie algebras and the exponential mapping is used. These choices are arbitrary, but once they are made, fixed. One possible choice of basis for the Lie algebra is, in the 4-vector representation, given by: J 1 = J 23 = − − J 32 = i ( 0 0 0 0 0 0 0 0 0 0 0 − − 1 0 0 1 0 ) , K 1 = J 01 = − − J 10 = i ( 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ) , J 2 = J 31 = − − J 13 = i ( 0 0 0 0 0 0 0 1 0 0 0 0 0 − − 1 0 0 ) , K 2 = J 02 = − − J 20 = i ( 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 ) , J 3 = J 12 = − − J 21 = i ( 0 0 0 0 0 0 − − 1 0 0 1 0 0 0 0 0 0 ) , K 3 = J 03 = − − J 30 = i ( 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 ) .