Electromagnetic tensor

Summary

In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime. The field tensor was first used after the four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows related physical laws to be written very concisely, and allows for the quantization of the electromagnetic field by Lagrangian formulation described below. Definition The electromagnetic tensor, conventionally labelled F, is defined as the exterior derivative of the electromagnetic four-potential, A, a differential 1-form: :F \ \stackrel{\mathrm{def}}{=}\ \mathrm{d}A. Therefore, F is a differential 2-form—that is, an antisymmetric rank-2 tensor field—on Minkowski space. In component form, :F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu. where

Official source

https://en.wikipedia.org/wiki/Electromagnetic_tensor

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (7)

Related publications

Related people

Related units

Related concepts (44)

In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time. In Albert Einstein's 1905 treatment, the theory is

In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the f

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to cons

Related concepts

Related courses (21)

Related courses

Related lectures (54)

Related lectures

Holographic imaging of electromagnetic fields via electron-light quantum interference

Gabriele Berruto, Fabrizio Carbone, Tatiana Latychevskaia, Tom Theodorus Antonius Lummen, Ivan Madan, Enrico Pomarico, Giovanni Maria Vanacore

Holography relies on the interference between a known reference and a signal of interest to reconstruct both the amplitude and the phase of that signal. With electrons, the extension of holography to the ultrafast time domain remains a challenge, although it would yield the highest possible combined spatiotemporal resolution. Here, we show that holograms of local electromagnetic fields can be obtained with combined attosecond/nanometer resolution in an ultrafast transmission electron microscope (UEM). Unlike conventional holography, where signal and reference are spatially separated and then recombined to interfere, our method relies on electromagnetic fields to split an electron wave function in a quantum coherent superposition of different energy states. In the image plane, spatial modulation of the electron energy distribution reflects the phase relation between reference and signal fields. Beyond imaging applications, this approach allows implementing quantum measurements in parallel, providing an efficient and versatile tool for electron quantum optics.

American Association for the Advancement of Science (AAAS)2019

We present an extension of a 2D cartesian electromagnetic and thermal model to achieve the optimal control of an industrial induction heating system. The control variables are the frequency and the power. We explain how to derive the discrete optimal control algorithm and show the numerical results we obtained for a specific case.

2004

Power line communication (PLC) is a well-known technique for data transmission over low-voltage power lines. The PLC signals have frequency bandwidth of about 1-30 MHz and they may cause electromagnetic interferences with services operating in the same frequency range. The regulation of electromagnetic radiation from PLC signals is currently subject of investigation in various international standardization bodies. This paper proposes a technique aiming at reducing the electromagnetic field radiated by indoor PLC signals, while not affecting the PLC signal itself. The basic idea is to take advantage of the additional ground conductor and inject a signal similar to the PLC signal into the ground-neutral line, but with a reversed phase. As a result, both the overall antenna mode- and transmission line mode-currents are significantly reduced, as well as the radiated electromagnetic fields. Experimental measurements are also carried out in a building and it is shown that the proposed technique allows for a significant reduction (up to 20 dB) of the PLC electromagnetic radiation in the considered frequency range (1-30 MHz)

2003