Comments on the energy-momentum tensor in non-commutative field theories

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 meth od yields a locally conserved yet non-symmetric energy-momentum tensor whos e trace does not vanish for massless fields. A non-symmetric tensor also go verns the response of the action to a general coordinate transformation. In non-commutative gauge theory, if translations are suitably combined with g auge 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, albe it non-symmetric, energy-momentum tensor. (C) 2001 Elsevier Science B.V. Al l rights reserved.