Thanks but can you suggest a book or something where i can understand this better, a good explanatory text perhaps.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.)
Was this helpful for you ? Either 1. or 2. should give you a starting point.
dextercioby said: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.
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.
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.
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.
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.
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.