The transformations of field operators illustrate the complementary role played by the finite-dimensional representations of the Lorentz group and the infinite-dimensional unitary representations of the Poincare group, witnessing the deep unity between mathematics and physics. For illustration, consider the definition an n -component field operator : A relativistic field operator is a set of n operator valued functions on spacetime which transforms under proper Poincaré transformations (Λ, a) according to