  We revise the tight binding approach to strained or curved graphene in the
presence of external probes such as Photoemission or Scanning Tunneling
Microscopy experiments. We show that extra terms arise in the continuum limit
of the tight binding Hamiltonian which can not be accounted for by changes in
the hopping parameters due to lattice deformations, encoded in the parameter
\beta. These material independent extra couplings are of the same order of
magnitude as the standard ones and have a geometric origin. They include
corrections to the position-dependent Fermi velocity and to a new vector field.
We show that the new vector field does not couple to electrons like a standard
gauge field and that no ? \beta-independent pseudomagnetic fields exist in
strained graphene.
