  Topological defects play an important role in physics of elastic media and
liquid crystals. Their kinematics is determined by constraints of topological
origin. An example is the glide motion of dislocations which has been
extensively studied by metallurgists. In a recent theoretical study dealing
with quantum dualities associated with the quantum melting of solids it was
argued that these kinematic constraints play a central role in defining the
quantum field theories of relevance to the description of quantum liquid
crystalline states of the nematic type. This forms the motivation to analyze
more thoroughly the climb constraints underlying the glide motions. In the
setting of continuum field theory the climb constraint is equivalent to the
condition that the density of constituent particles is vanishing and we derive
a mathematical definition of this constraint which has a universal status. This
makes possible to study the kinematics of dislocations in arbitrary space-time
dimensions and as an example we analyze the restricted climb associated with
edge dislocations in 3+1D. Very generally, it can be shown that the climb
constraint is equivalent to the condition that dislocations do not communicate
with compressional stresses at long distances. However, the formalism makes
possible to address the full non-linear theory of relevance to short distance
behaviors where violations of the constraint become possible.

Strongly Correlated Electrons;Materials Science