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Weinberg 5.9.34

Not a four vector? So the vector potential in the development that follows is not a vector, not Lorentz invariant, and most significantly, not generally covariant in this universe.

If ##a## is not a vector in the construction of a Lagrangian, either the action is not a scalar or the charge-current density is not a tensor, or both.

If we brush this under the carpet, a Lagrangian constructed to conserve charge is either not the Lagrangian of a conserved quantity (##dj \neq 0##) or the Lagrangian density is frame dependent, or both.

Is this later resolved?

"[...] Using this together with Eq. 5.9.23 gives the general antisymmetric tensor field for massless particles of helicity ##\pm 1## in the form ##f_{\mu\nu} = \partial_{ [ \mu } a_{ \nu ] }##. Note that this is a tensor even though ##a_{\mu}## is not a 4-vector."

Not a four vector? So the vector potential in the development that follows is not a vector, not Lorentz invariant, and most significantly, not generally covariant in this universe.

If ##a## is not a vector in the construction of a Lagrangian, either the action is not a scalar or the charge-current density is not a tensor, or both.

If we brush this under the carpet, a Lagrangian constructed to conserve charge is either not the Lagrangian of a conserved quantity (##dj \neq 0##) or the Lagrangian density is frame dependent, or both.

Is this later resolved?

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