Energy-momentum tensor for electromagnetism

[nikhilb1997]

Homework Statement

Derive
T^μν=F^μλF^ν_λ-1/4η^μνF^λθF_λθ
From
\mathcal{L}=1/4F_{μν}F^{μν}+A_μJ^μ

Homework Equations

Above

3. The Attempt at a Solution
The first term of the given equation and the second term of the equation to prove are i believe the same.i know, J^μ=\partial_νF^{μν} But I need an explanation for the equivalence of the remaining term.
Thank You

 

[dextercioby]

1. In the absence of gravity T follows from L from the Noether theorem and the Belinfante symmetrization procedure.

2. In the presence of gravity T follows from L directly (even without the coupling to charged scalar matter).

Both parts are (advanced) textbook stuff in either of the 3 subjects: classical electrodynamics or classical/quantum field theory (1.), general relativity (2.)

Was this helpful for you ? Either 1. or 2. should give you a starting point.

 

[nikhilb1997]

1. In the absence of gravity T follows from L from the Noether theorem and the Belinfante symmetrization procedure.

2. In the presence of gravity T follows from L directly (even without the coupling to charged scalar matter).

Both parts are (advanced) textbook stuff in either of the 3 subjects: classical electrodynamics or classical/quantum field theory (1.), general relativity (2.)

Was this helpful for you ? Either 1. or 2. should give you a starting point.

Thanks but can you suggest a book or something where i can understand this better, a good explanatory text perhaps.

 

[dextercioby]

For the GR stuff, check section 28, page 54 from Dirac's brochure on GR (I chose Dirac's book as being the easiest path to the wanted reference).
For SR http://en.wikipedia.org/wiki/Belinfante–Rosenfeld_stress–energy_tensor. I can't find a book reference.

 

[nikhilb1997]

For the GR stuff, check section 28, page 54 from Dirac's brochure on GR (I chose Dirac's book as being the easiest path to the wanted reference).
For SR http://en.wikipedia.org/wiki/Belinfante–Rosenfeld_stress–energy_tensor. I can't find a book reference.

Thanks