  A Poincar\'e multiplet of mass eigenstates $\bigl(P^2 - m^2\bigr)\Psi = 0$
cannot be a subspace of a space with a $D$-vector position operator
$X=(X_0,\dots X_{D-1})$: the Heisenberg algebra $[P^m, X_n] = i \delta^m{}_n$
implies by a simple argument that each Poincar\'e multiplet of definite mass
vanishes.
  The same conclusion follows from the Stone-von Neumann theorem.
  In a quantum theory the constraint of an absolutely continuous spectrum to a
lower dimensional submanifold yields zero even if Dirac's treatment of the
corresponding classical constraint defines a symplectic submanifold with a
consistent corresponding quantum model. Its Hilbert space is not a subspace of
the unconstrained theory. Hence the operator relations of the unconstrained
model need not carry over to the constrained model.
  Our argument excludes quantized worldline models of relativistic particles
and the physical states of the covariant quantum string.
  We correct misconceptions about the generators of Lorentz transformations
acting on particles.
