  We investigate a formulation of Poincar\'e invariant quantum mechanics where
the dynamical input is Euclidean invariant Green functions or their generating
functional. We argue that within this framework it is possible to calculate
scattering observables, binding energies, and perform finite Poincar\'e
transformations without using any analytic continuation. We demonstrate, using
a toy model, how matrix elements of $e^{-\beta H}$ in normalizable states can
be used to compute transition matrix elements for energies up to 2 GeV. We
discuss some open problems.
