  We investigate the single hole dynamics in the triangular t-J model. We study
the structure of the hole spectral function, assuming the existence of a 120
magnetic Neel order. Within the self-consistent Born approximation (SCBA) there
is a strong momentum and t sign dependence of the spectra, related to the
underlying magnetic structure and the particle-hole asymmetry of the model. For
positive t, and in the strong coupling regime, we find that the low energy
quasiparticle excitations vanish outside the neighbourhood of the magnetic
Goldstone modes; while for negative t the quasiparticle excitations are always
well defined. In the latter, we also find resonances of magnetic origin whose
energies scale as (J/t)^2/3 and can be identified with string excitations. We
argue that this complex structure of the spectra is due to the subtle interplay
between magnon-assisted and free hopping mechanisms. Our predictions are
supported by an excellent agreement between the SCBA and the exact results on
finite size clusters. We conclude that the conventional quasiparticle picture
can be broken by the effect of geometrical magnetic frustration.
