Topological Quantum Field Theory Seminar   RSS

09/10/2006, 11:00 — 12:00 — Room P3.10, Mathematics Building
Mark Gotay, Univ. of Hawai at Manoa

Stress-Energy-Momentum Tensors

J. Marsden and I present a new method of constructing a stress-energy-momentum tensor for a classical field theory based on covariance considerations and Noether theory. Our stress-energy-momentum tensor Tμ ν is defined using the (multi)momentum map associated to the spacetime diffeomorphism group. The tensor Tμ ν is uniquely determined as well as gauge-covariant, and depends only upon the divergence equivalence class of the Lagrangian. It satisfies a generalized version of the classical Belinfante-Rosenfeld formula, and hence naturally incorporates both the canonical stress-energy-momentum tensor and the "correction terms" that are necessary to make the latter well behaved. Furthermore, in the presence of a metric on spacetime, our Tμν coincides with the Hilbert tensor and hence is automatically symmetric.

  1. Gotay, M. J. and J. E. Marsden [1992], Stress-energy-momentum tensors and the Belinfante-Rosenfeld formula, Contemp. Math. 132, 367-391.
  2. Forger, M. and H. Römer [2004], Currents and the energy-momentum tensor in classical field theory: A fresh look at an old problem, Ann. Phys. 309, 306-389.

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Current organizers: José MourãoRoger Picken, Marko Stošić


FCT Projects PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry, PTDC/MAT-PUR/31089/2017, Higher Structures and Applications.