  We give a non-technical description of the differences of quantisation of the
bosonic string between the usual Fock-space approach and the treatment inspired
by methods of loop quantum gravity termed the LCQ string. We point out the role
of covariant states with continuous representations of the Weyl operators
versus invariant states leading to discontinuous polymer representations. In
the example of the harmonic oscillator we compare the optical absorption
spectrum for the two quantisations and find that the question of
distinguishability depends on the order in which limits are taken: For a fixed
UV cut-off restricting the Hilbert space to a finite dimensional subspace the
spectra can be made arbitrarily similar by an appropriate choice of state.
However, if the states are chosen first, they differ at high frequencies.
