# Energy-momentum tensor for electromagnetism

• nikhilb1997
In summary: I'll check it out. In summary, the equation Tμν=FμλFνλ-1/4ημνFλθFλθ can be derived from the equation \mathcal{L}=1/4F_{μν}F^{μν}+A_μJ^μ using the Noether theorem and the Belinfante symmetrization procedure in the absence of gravity, and directly in the presence of gravity. This is a concept in classical electrodynamics, classical/quantum field theory, and general relativity, and can be found in textbooks such as Dirac's brochure on GR and through online resources.
nikhilb1997

## Homework Statement

Derive
Tμν=FμλFνλ-1/4ημνFλθFλθ
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, Jμ=$$\partial_νF^{μν}$$
But I need an explanation for the equivalence of the remaining term.
Thank You

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.)

dextercioby said:
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.)

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

## What is the energy-momentum tensor for electromagnetism?

The energy-momentum tensor for electromagnetism is a mathematical object that describes the distribution of energy and momentum in an electromagnetic field. It is a symmetric tensor with 4 rows and 4 columns, representing the 4-dimensional spacetime in which electromagnetism operates.

## How is the energy-momentum tensor derived for electromagnetism?

The energy-momentum tensor for electromagnetism is derived from the electromagnetic Lagrangian density, which is a function that describes the dynamics of electromagnetic fields. By applying the principles of variational calculus, the energy-momentum tensor can be obtained as the functional derivative of the Lagrangian with respect to the metric tensor.

## What are the components of the energy-momentum tensor for electromagnetism?

The energy-momentum tensor for electromagnetism has 10 independent components, which can be grouped into two sets: the energy density and energy flux components, and the momentum density and momentum flux components. These components represent the flow of energy and momentum in different directions in the electromagnetic field.

## What is the significance of the energy-momentum tensor in electromagnetism?

The energy-momentum tensor is an important tool in understanding the behavior of electromagnetic fields. It allows us to calculate the energy and momentum of the electromagnetic field, and to determine how these quantities are transferred and conserved. Additionally, it is a key component in the Einstein field equations, which describe the relationship between matter and spacetime in general relativity.

## How is the energy-momentum tensor used in practical applications?

The energy-momentum tensor has various practical applications, such as in the study of gravitational waves, black holes, and cosmology. It is also used in the analysis of particle collisions in high energy physics experiments. Additionally, it is a fundamental concept in the development of advanced technologies such as particle accelerators and electromagnetic propulsion systems.

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