On the geometric origin of the energy-momentum tensor improvement terms
arXiv:2503.21609 · doi:10.1103/wby2-d33f
Abstract
In a flat background, the canonical energy momentum tensor of Lorentz and conformally invariant matter field theories can be improved to a symmetric and traceless tensor that gives the same conserved charges. We argue that the geometric origin of this improvement process is unveiled when the matter theory is coupled to Metric-Affine Gravity. In particular, we show that the Belinfante-Rosenfeld improvement terms correspond to the matter theory's hypermomentum. The improvement terms in conformally invariant matter theories are also related to the hypermomentum however a general proof would require an extended investigation. We demonstrate our results through various examples, such as the free massless scalar, the Maxwell field, Abelian -forms, the Dirac field and a non-unitary massless scalar field. Possible applications of our method for theories that break Lorentz or special conformal invariance are briefly discussed.
arXiv commentv1:1+41 pages, Latex, v2: PRD version
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