The relativistic invariance of a quantum theory means that the observables (probabilities, expectation values and ensemble averages) have the same values in all inertial coordinate systems. Since different inertial coordinate systems are related by inhomogeneous Lorentz transformations (Poincaré transformations), this requires that the Poincaré group is a symmetry group of the theory. Wigner and Bargmann showed that this symmetry must be realized by a unitary representation of the connected component of the Poincaré group on the Hilbert space of the quantum theory. The Poincaré symmetry is a dynamical symmetry because Poincaré transformations mix both space and time variables. The dynamical nature of this symmetry is most easily seen by noting that the Hamiltonian appears on the right-hand side of three of the commutators of the Poincaré generators, [ K j , P k ] = i δ δ j k H , where P k are components of the linear momentum and K j are components of rotation-less boost generators. If the Hamiltonian includes interactions, i.e. H = H 0 + V , then the commutation relations cannot be satisfied unless at least three of the Poincaré generators also include interactions.