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arXiv · 2503.21609

On the geometric origin of the energy-momentum tensor improvement terms

Damianos Iosifidis·Manthos Karydas·Anastasios Petkou·Konstantinos Siampos
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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 $p$-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.

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Damianos Iosifidis, Manthos Karydas, Anastasios Petkou, Konstantinos Siampos. 2025-07-08. On the geometric origin of the energy-momentum tensor improvement terms. https://doi.org/10.1103/wby2-d33f

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