Covariant Formulation of Electrodynamics
a new positive energy theorem for general relativity. In the field theory, the energy is given by E = R hTtti, and so as in the general discussion above, one is considering states for which the expectation value of a particular operator, i.e., the stress-energy tensor, is nonvanishing. Dec 15, 2000 · The traceless stress tensor formulation can be easily extended to other constitutive models and this is demonstrated here with the Phan-Thien–Tanner equation: (24) f(tr (τ))+ τ +λ τ ∇ =2η D, where f is a function of the trace of stress tensor which can take the following forms: f(tr (τ))=1+ λε η tr (τ) or f(tr (τ))= exp λε η Quite literally, a traceless tensor T is one such that Tr(T)=0. The trace of a tensor (in index notation) can be thought of as contracting one of a tensor’s indices with another: i.e. in general relativity, the Ricci curvature scalar is given by t Aug 01, 1977 · ANNALS OF PHYSICS 106, 279-321 (1977) Regularization of the Stress-Energy Tensor for Vector and Scalar Particles Propagating in a General Background Metric* STEPHEN L. ADLER, JUDY LIEBERMAN, AND YEE TACK NG The Institute for Adranced Studv, Princeton, New Jersey 08540 Received August 3, 1976; revised November 23, 1976 We study the regularization of the stress-energy tensor for massless vector
stress-energy tensor as before, namely by (6), it cannot be expected that we still have τk i,k = 0, but neither τk i;k, since, in general, τ k i is not even a covariant object (nevertheless, we will continue to refer to it as canonical tensor) and therefore the use of a covariant derivative does not seem to make much sense.
The electromagnetic energy tensor The right-hand side of Eq. represents the rate per unit volume at which energy is transferred from the electromagnetic field to charged particlesIt is clear, therefore, that Eq. is an energy conservation equation for the electromagnetic field (see Sect. 8.2)The proper-3-scalar can be identified as the energy density of the electromagnetic field, whereas the proper-3-vector is the energy flux Regularization of the stress-energy tensor for vector and
A traceless stress tensor formulation for viscoelastic
IDEALS @ Illinois: Improvement of stress-energy tensor