  Reviewing the construction of induced representations of the Poincar\'e group
of four-dimensional spacetime we find all massive representations, including
the ones acting on interacting many-particle states. Massless momentum
wavefunctions of non-vanishing helicity turn out to be more precisely sections
of a U(1)-bundle over the massless shell, a property which to date was
overlooked in bracket notation. Our traditional notation enables questions
about square integrability and smoothness. Their answers complete the picture
of relativistic quantum physics.
  Frobenius' reciprocity theorem prohibits massless one-particle states with
total angular momentum less than the modulus of the helicity. There is no
two-photon state with J=1, explaining the longevity of orthopositronium.
  Partial derivatives of the momentum wave functions are no operators which can
be applied to massless states Psi with nonvanishing helicity. They allow only
for covariant, noncommuting derivatives. The massless shell has a
noncommutative geometry with helicity being its topological charge. A spatial
position operator for Psi which constitutes Heisenberg pairs with the spatial
momentum, is excluded by the smoothness requirement of the domain of the
Lorentz generators.

High Energy Physics - Theory