  Relativistic invariance in Euclidean formulations of quantum mechanics is
discussed. Relativistic treatments of quantum theory are needed to study
hadronic systems at sub-hadronic distance scales. Euclidean formulations of
relativistic quantum mechanics have some computational advantages. In the
Euclidean representation the physical Hilbert space inner product is expressed
in terms of Euclidean space-time variables with no need for any analytic
continuation. The identification of the complex Euclidean group with the
complex Poincar\'e group relates the infinitesimal generators of both groups.
In this work explicit representations of the Poincar\'e generators in Euclidean
space-time variables for all positive-mass positive-energy irreducible
representations of the Poincar\'e group are derived. The commutation relations
are checked, both hermiticity and self-adjointness are established, and
reflection positivity of the kernels is verified.
