Speaker
Description
The main purpose of this work is to obtain the Electromagnetic Stress-Energy Tensor in a medium for a nonlocal theory. In order to get it, we generalise Minkowski electrodynamics to dispersive media. As a consequence of this generalisation, the Lagrangian density becomes non-local due to the non-local dependencies of the magnetic permeability and electric permittivity. This leads a convolution product in the Lagrangian where the field at point 'x' depends on the values of the field at any point in spacetime. Then, we derive the field equations and, applying the Noether's theorem, the conserved energy-momentum tensor. Because non-local Lagrangians are seldom found in textbooks, we devote a non-local formalism to outline the derivation of the field equations and Noether's theorem. For that, the procedure is the following: First, the non-local Lagrangian is converted into an infinite order Lagrangian (that depends on derivatives of the field of any order). Then, the equations of motion and Noether's theorem are derived as though it was an order-n Lagrangian. Finally, we extend n to infinite and the outcomes that appear contain formal series that can be summed by the techniques that we have developed. To conclude, we study the obtained Belinfante Stress-Energy Tensor for plane wave solutions for a dispersive medium.
