  Bound and scattering state Schr\"odinger functions of nonrelativistic quantum
mechanics as representation matrix elements of space and time are embedded into
residual representations of spacetime as generalizations of Feynman
propagators. The representation invariants arise as singularities of rational
representation functions in the complex energy and complex momentum plane. The
homogeneous space $GL(2,C)/U(2)$ with rank 2, the orientation manifold of the
unitary hypercharge-isospin group, is taken as model of nonlinear spacetime.
Its representations are characterized by two continuous invariants whose ratio
will be related to gauge field coupling constants as residues of the related
representation functions. Invariants of product representations define unitary
Poincar\'e group representations with masses for free particles in tangent
Minkowski spacetime.
