Energy-momentum tensor Definition and 61 Threads

I have studied Jackson, Landau, and Barut textbooks on electrodynamics, together with Weinberg's Gravitation and Cosmology textbook, and I find that the usual action S = S_f + S_m + S_{mf} is inconsistent and not well-defined. For instance, what is the meaning of S_f? A free-field term? Or...

Hi This might be a stupid question, so I hope you are patient with me. When I look for the definition of the energy-momentum tensor in terms of the Lagrangian density, I find two different (?) definitions: {T^\mu}_\nu = \frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)}\partial_\nu...

Okay so I have: Eqn1) Tij=\rhouiuj-phij = \rhouiuj-p(gij-uiuj) Where Tij is the energy-momentum tensor, being approximated as a fluid with \rho as the energy density and p as the pressure in the medium. My problem: Eqn2) Trace(T) = Tii = gijTij = \rho-3p My attempt: Tr(T) = Tii...

Homework Statement The problem is conveniently located here: http://www.dur.ac.uk/resources/cpt/graduate/lectures/mscps.pdf Problem no. 31. There's even a solution, here: http://www.dur.ac.uk/resources/cpt/graduate/lectures/grsolns.pdf However, I don't understand the solution...

Electrodynamics force is f_i=F_{ik}j^k=F_{ik}\partial_j F^{jk}. I claim that the only way to obtain the Maxwell energy-momentum tensor T_i^j=-F_{ik}F^{jk}+\delta_i^jF_{kl}F^{kl}/4 is to write the force as a divergence: f_i=-\partial_jT_i^j.

I'm studying General Relativity and facing several problems. We know that energy-momentum must be Lorentz invariant in locally inertial coordinates. I am not sure I understand this point clearly. What is the physics behind?

Hi all, In Polchinski's string theory text he asserts (volume 1, section 3.4) that the trace of the energy-momentum tensor of a classically scale -invariant theory becomes proportional in the quantum theory to the beta function of the coupling, as a general point of QFT. This makes a kind of...

Hi, I believe you can use the "energy-momentum tensor" to express the conservation of both energy and momentum for fields (\partial_{\mu} T^{\mu \nu} = 0). But I'm wondering: why's a tensor needed, specifically, to describe this conservation of energy and momentum for fields? For particles, I...

Hi I have a small subtle problem with the sign of the energy-momentum tensor for a scalar field as derived by varying the metric (s.b.). I would appreciate very much if somebody could help me on my specific issue. Let me describe the problem in more detail: I conform to the sign convention...

I was wondering if someone could clarify something that I read in a book (Nakahara's book on Geometry, Topology, Physics). In the section on the Einstein-Hilbert action, the author defines the energy-momentum tensor as \delta S_M = \frac{1}{2} \int T^{\mu \nu} \delta g_{\mu \nu} \sqrt{- g} d^4...

Is it correct that the only way to have a theory of gravitation that fulfills the equivalence principle is to make use of a tensor as the source of gravity (and not a scalar or a vector, for example)? How can this be proven?