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The electromagnetic field admits a coordinate-independent geometric description, and Maxwell's equations expressed in terms of these geometric objects are the same in any spacetime, curved or not. Also, the same modifications are made to the equations of flat Minkowski space when using local coordinates that are not rectilinear.
An electromagnetic field having energy and momentum also generates curvature in spacetime. Maxwell's equations in curved spacetime can be obtained by replacing the derivatives in the equations in flat spacetime with covariant derivatives .
This gives the fields in a particular reference frame; if the reference frame is changed, the components of the electromagnetic tensor will transform covariantly, and the fields in the new frame will be given by the new components. In contravariant matrix form with metric signature (+,-,-,-),
The Berry curvature per solid angle is given by ¯ = / = /. In this case, the Berry phase corresponding to any given path on the unit sphere S 2 {\displaystyle {\mathcal {S}}^{2}} in magnetic-field space is just half the solid angle subtended by the path.
An electromagnetic field (also EM field) is a physical field, mathematical functions of position and time, representing the influences on and due to electric charges. [1] The field at any point in space and time can be regarded as a combination of an electric field and a magnetic field .
The gauge field becomes an essential part of the description of a mathematical configuration. A configuration in which the gauge field can be eliminated by a gauge transformation has the property that its field strength (in mathematical language, its curvature) is zero everywhere; a gauge theory is not limited to these configurations. In other ...
The E field and B field vary in space and time. Electromagnetic (EM) fields affect the motion of electrically charged matter: due to the Lorentz force. In this way, EM fields can be detected (with applications in particle physics, and natural occurrences such as in aurorae). In relativistic form, the Lorentz force uses the field strength tensor ...
This is often described by saying that the electric field and magnetic field are two interrelated aspects of a single object, called the electromagnetic field. Indeed, the entire electromagnetic field can be represented in a single rank-2 tensor called the electromagnetic tensor; see below.