One may also introduce a magnetic electromagnetic tensor, usually denoted by " F uv ", but in this case by " iF uv ".
12.
The color charge four-current is the source of the gluon field strength tensor, analogous to the electromagnetic four-current as the source of the electromagnetic tensor.
13.
In special relativity, the electric and magnetic fields must be written in the form of a tensor so they transform correctly under Lorentz transformations-achieved by the electromagnetic tensor.
14.
Cut off the last row and column from the electromagnetic tensor ( and B z becomes the one-dimensional B ) . talk ) 17 : 57, 4 February 2010 ( UTC)
15.
The electromagnetic tensor, conventionally labelled " F ", is defined as the exterior derivative of the electromagnetic four-potential, " A ", a differential 1-form:
16.
Here, " ? " " ?? " } } and stand for the Lorentz group generators in the Dirac space, and the electromagnetic tensor respectively, while is the electromagnetic four-potential.
17.
To obtain the field equations the electromagnetic tensor in the Lagrangian density needs to be replaced by its definition in terms of the 4-potential " A ", and its this potential which enter the Euler-Lagrange equations.
18.
For the abelian case, " n " = 1, and the vector bundle is one-dimensional; the commutator vanishes, and the above can then be recognized as the electromagnetic tensor in more or less standard physics notation.
19.
For example, when measuring the electric and magnetic fields produced by an accelerating charge, the values of the fields will depend on the coordinate system used, but the fields are regarded as having an independent existence, this independence represented by the electromagnetic tensor.
20.
Although Cartesian tensors do not occur in the theory of relativity; the tensor form of orbital angular momentum "'J "'enters the spacelike part of the relativistic angular momentum tensor, and the above tensor form of the magnetic field "'B "'enters the spacelike part of the electromagnetic tensor.
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