  A continuum model to study the influence of dislocations on the electronic
properties of condensed matter systems is described and analyzed. The model is
based on a geometrical formalism that associates a density of dislocations with
the torsion tensor and uses the technique of quantum field theory in curved
space. When applied to two-dimensional systems with Dirac points like graphene
we find that dislocations couple in the form of vector gauge fields similar to
these arising from curvature or elastic strain. We also describe the ways to
couple dislocations to normal metals with a Fermi surface.
