Euclidean relativistic quantum mechanics I

We introduce a formulation of relativistic quantum mechanics where the dynamical input is Euclidean generating functionals or Green functions. We discuss how dynamical calculations can be performed in this framework without analytic continuation. We discuss the structure of model generating functionals, the construction of the Hilbert space, the Poincar\'e Lie Algebra, one particle eigenstates, and representations of finite Poincar\'e transformations.