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...
Homework Statement
In Minkowski space, we are given a scalar field \phi with action
S= \int d\Omega (\frac{-1}{2}\phi^{,a}\phi_{,a} - \frac{1}{2}m^2\phi^2)
We need to calculate the "translation-invariance" energy-momentum tensor:
T^a_b = \frac{\partial \mathcal{L}}{\partial \phi_{,a}}...
Homework Statement
1) Use conservation of Energy-Momentum Tensor to show that
\partial_{0}^{2}T^{00}=\partial_{m}\partial_{n}T^{mn}
Homework Equations
\partial_{\nu}T^{\mu\nu}=0
The Attempt at a Solution
\partial_{\nu}T^{\mu\nu}=0...
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?