where is the trace of the energy-momentum-stress-shear tensor of some astrophysical system. (As an aside, observe the Galileon does not couple to the photon at this order since the latter’s stress tensor is traceless; i.e., it violates the equivalence principle.)
The electromagnetic energy tensor Consider a continuous volume distribution of charged matter in the presence of an electromagnetic field. Let there be particles per unit proper volume (unit volume determined in the local rest frame), each carrying a charge . Consider an inertial frame in which the 3-velocity field of the particles is . A quick summary of the traceless version of general relativity. I was just introduced to the concept of a "traceless version" of general relativity through a pre-print of John Barrow and Spiros Cotsakis, whose viability coincidentally was something that I was wondering about last week. The local behavior of the Maxwell tensor, or of the relativistic symmetrical stress-energy tensor, is extremely important because as shown by, for example, Deutsch and Candelas [9] with the help of Green functions techniques, as we approach the boundaries we find strong divergencies that cannot be simply removed by usual renormalization procedures. The prescription, however, is not a unique one, since the conventionally renormalized stress-energy tensor contains an undetermined multiple of a term, which can be formally reinterpreted as arising from an addition to the gravitational action which is quadratic in the Weyl curvature tensor.
Dec 15, 2000
9. Stress-Energy-Momentum Tensor of Matter Fields 10. Stress-Energy-Momentum Tensors of Gauge Potentials 11. Stress-Energy-Momentum Tensors of Proca Fields 12. Topological Gauge Theories Part 2. 13. Reduced Second Order Lagrangian Formalism 14. Conservation Laws in Einstein’s Gravitation Theory 15. First Order Palatini Formalism 16. Stress Improvement of stress-energy tensor using space-time In 1970 Callan, Coleman, and Jackiw found that it is always possible to improve the symmetric stress-energy tensor of a renormalizable relativistic field theory over (3+1)-dimensional flat space-time manifold. The improved stress-energy tensor defines the same field energy- momentum and angular momentum as the conventional tensor, and it is traceless for a non-interacting field theory when all
object encoding the relation among the energy density, the energy ux, the momentum density and the momentum ux or stress. This quantity is the so-called energy-momentum-stress tensor. Let’s construct it. 1Note that in the electromagnetic case, the total electric charge Q= R ˆed3xis Lorentz invariant.
The improved stress-energy tensor defines the same field energy-momentum and angular momentum as the conventional tensor, and it is traceless for a non-interacting field theory when all coupling constants are physically dimensionless. Field Theory – Struggles In Physics where is the trace of the energy-momentum-stress-shear tensor of some astrophysical system. (As an aside, observe the Galileon does not couple to the photon at this order since the latter’s stress tensor is traceless; i.e., it violates the equivalence principle.) NOETHER’S THEOREM - TRACELESS STRESS-ENERGY … the stress-energy tensor. T =0 (14) That is, the stress-energy tensor is traceless in this case. Notice that this result doesn’t depend on the form of the Lagrangian or the stress-energy tensor; it is derived purely from the requirement that the action be invariant under the given transformations. Number-Flux Vector and Stress-Energy Tensor MassachusettsInstituteofTechnology DepartmentofPhysics Physics8.962 Spring2002 Number-Flux Vector and Stress-Energy Tensor °c2000,2002EdmundBertschinger.