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\end{equation}  There are now hypercomplex four potentials from the real potential such that  $A_\mu \to A_\mu + B_mu B_\mu  i + \Gamma_\mu j + \Delta_\mu k$ k$.  Now, as usually defined we can create the tensor \begin{equation}  H_{\mu \nu} = (dA)_{\mu \nu}= \partial_\mu A_\nu - \partial_\nu A_\mu