  We investigate the T(3)-gauge theory of static dislocations in continuous
solids. We use the most general linear constitutive relations bilinear in the
elastic distortion tensor and dislocation density tensor for the force and
pseudomoment stresses of an isotropic solid. The constitutive relations contain
six material parameters. In this theory both the force and pseudomoment
stresses are asymmetric. The theory possesses four characteristic lengths l1,
l2, l3 and l4 which are given explicitely. We first derive the
three-dimensional Green tensor of the master equation for the force stresses in
the translational gauge theory of dislocations. We then investigate the
situation of generalized plane strain (anti-plane strain and plane strain).
Using the stress function method, we find modified stress functions for screw
and edge dislocations. The solution of the screw dislocation is given in terms
of one independent length l1=l4. For the problem of an edge dislocation, only
two characteristic lengths l2 and l3 arise with one of them being the same
l2=l1 as for the screw dislocation. Thus, this theory possesses only two
independent lengths for generalized plane strain. If the two lengths l2 and l3
of an edge dislocation are equal, we obtain an edge dislocation which is the
gauge theoretical version of a modified Volterra edge dislocation. In the case
of symmetric stresses we recover well known results obtained earlier.
