  The prospects are explored for testing Lorentz and CPT symmetry in the
top-quark sector. We present the relevant Lagrange density, discuss physical
observables, and describe the signals to be sought in experiments. For
top-antitop pair production via quark or gluon fusion with subsequent
semileptonic or hadronic decays, we obtain the matrix element in the presence
of Lorentz violation using the narrow-width approximation. The issue of testing
CPT symmetry in the top-quark sector is also addressed. We demonstrate that
single-top production and decay is well suited to a search for CPT violation,
and we present the matrix elements for single-top production in each of the
four tree-level channels. Our results are applicable to searches for Lorentz
violation and studies of CPT symmetry in collider experiments, including
notably high-statistics top-antitop and single-top production at the Large
Hadron Collider.
