The density of electric current \ mathfrak { J } ^ \ mu ( " e . g . ", \ mathfrak { J } ^ 2 is the amount of electric charge crossing the 3-volume element d x ^ 3 \, d x ^ 4 \, d x ^ 1 divided by that element do not use the metric in this calculation ) is a contravariant vector density of weight + 1.
2.
The density of Lorentz force \ mathfrak { f } _ \ mu ( " i . e . ", the linear momentum transferred from the electromagnetic field to matter within a 4-volume element d x ^ 1 \, d x ^ 2 \, d x ^ 3 \, d x ^ 4 divided by that element do not use the metric in this calculation ) is a covariant vector density of weight + 1 . \ mathfrak { J } ^ \ mu .-->
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