This can be easily generalized: If G is a connected Lie group of symmetries of Q satisfying the same weak continuity conditions, then the action of any element g of G is given by a unitary operator U : g ⋅ ⋅ E = U g E U g ∗ ∗ . This mapping g → U g is known as a projective representation of G. The mappings S → U * g S U g are reversible quantum operations.