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User:EverettYou/Classical Electrodynamics

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Lorentz Covariant Notations

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Space-time coordinates , and their partial derivatives . The gauge potentials (connections) .

The indices can be raised or lowered by the Minkowski metric

Dynamics of Electromagnetic Field

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Action

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Lagrangian density

,

where the kernel reads

.

In terms of momentum ,

,

where .