Abstract
In affirmative, the equivariant inverse problem for Maxwell-type Euler–Lagrange expressions is solved. This allows the proof of the uniqueness of the Maxwell equations.
Highlights
It is very well known that Maxwell equations can be written in covariant form as!
The Maxwell equations can be deduced from a variational principle as follows
From a variation of tPi we obtain as Euler-Lagrange equations, ( 1.5)
Summary
It is very well known that Maxwell equations can be written in covariant form as!. where Fij is a skew-symmetric tensor and *Fij = 1JijhkF hk. If. The left-hand side of ( 1.1) has two properties of covariance: (1) by a transformation ofcoordinates it changes as a vector; and (2) by a change of gauge, i.e., by a transformation ofthe type tPi -+tPi + f/J,i> where f/J is a scalar, it is invariant. The left-hand side of ( 1.1) has two properties of covariance: (1) by a transformation ofcoordinates it changes as a vector; and (2) by a change of gauge, i.e., by a transformation ofthe type tPi -+tPi + f/J,i> where f/J is a scalar, it is invariant These properties are possessed by the Lagrangian ( 1.6).
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