What's the adjoint of the covariant derivative?

Question

The covariant derivative being the curly "d" with a low "mu" beside it. And is the covariant a row or column vector? And so is the adjoint the opposite?

Answer 1

The covariant derivative d_mu is a column vector. Its adjoint is d*^mu, often called the Hermitian conjugate and it is its row-vector, complex conjugate counterpart.

Answer 2

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