  In a non-commutative field theory, the energy-momentum tensor obtained from
the Noether method needs not be symmetric; in a massless theory, it needs not
be traceless either. In a non-commutative scalar field theory, the method
yields a locally conserved yet non-symmetric energy-momentum tensor whose trace
does not vanish for massless fields. A non-symmetric tensor also governs the
response of the action to a general coordinate transformation. In
non-commutative gauge theory, if translations are suitably combined with gauge
transformations, the method yields a covariantly constant tensor which is
symmetric but only gauge covariant. Using suitable Wilson functionals, this can
be improved to yield a locally conserved and gauge invariant, albeit
non-symmetric, energy-momentum tensor.
