  We derive conservation and balance laws for the translational gauge theory of
dislocations by applying Noether's theorem. We present an improved
translational gauge theory of dislocations including the dislocation density
tensor and the dislocation current tensor. The invariance of the variational
principle under the continuous group of transformations is studied. Through
Lie's-infinitesimal invariance criterion we obtain conserved translational and
rotational currents for the total Lagrangian made up of an elastic and
dislocation part. We calculate the broken scaling current. Looking only on one
part of the whole system, the conservation laws are changed into balance laws.
Because of the lack of translational, rotational and dilatation invariance for
each part, a configurational force, moment and power appears. The corresponding
J, L and M integrals are obtained. Only isotropic and homogeneous materials are
considered and we restrict ourselves to a linear theory. We choose constitutive
laws for the most general linear form of material isotropy. Also we give the
conservation and balance laws corresponding to the gauge symmetry and the
addition of solutions. From the addition of solutions we derive a reciprocity
theorem for the gauge theory of dislocations. Also, we derive the conservation
laws for stress-free states of dislocations.
