# Energy-momentum tensor for electromagnetism

1. Jan 1, 2013

### nikhilb1997

1. The problem statement, all variables and given/known data
Derive
Tμν=FμλFνλ-1/4ημνFλθFλθ
From
$$\mathcal{L}=1/4F_{μν}F^{μν}+A_μJ^μ$$

2. Relevant 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, Jμ=$$\partial_νF^{μν}$$
But I need an explanation for the equivalence of the remaining term.
Thank You

2. Jan 1, 2013

### 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.)

3. Jan 1, 2013

### nikhilb1997

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

4. Jan 2, 2013

5. Jan 2, 2013