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The general aim of this paper is to extend the Modal-Hamiltonianinterpretation of quantum mechanics to the case of relativistic quantummechanics with gauge U(1) elds. In this case we propose that the actual- valuedobservables are the Casimir operators of the Poincar\'e group and of the groupU(1) of the internal symmetry of the theory. Moreover, we also show that themagnitudes that acquire actual values in the relativistic and in thenon-relativistic cases are correctly related through the adequate limit.

Modal Hamiltonian interpretation of quantum mechanics and Casimir operators: the road towards quantum field theory