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$ \ F^{\mu\nu}$ and the Hodge dual $\tilde F_{\rho\sigma}$ these are two tensors, related by $\epsilon_{\rho\sigma\mu\nu }$. My question is, is there any physical difference between them( I am aware their matrix form)?

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They're related via the electromagnetic duality transformation ${\bf E} \to {\bf B},\ {\bf B} \to -{\bf E}$.

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