Why we still consider the case of non-minimal coupling? And I don't really understand the motivation of coupling. In general relativity, the non-minimal coupling violates the principle of equivalence. In gauge field, the minimal coupling represents the covariant derivative of fiber bundles and is consistent with gauge redundancy. So it seems that there is no reason for us to consider the non-minimal coupling, except the conformal coupling. So why are there so many models of non-minimal coupling?
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