It has been sometime since I have been thinking about this question and I have been quite successful in confusing myself.(adsbygoogle = window.adsbygoogle || []).push({});

In Einstein's General Relativity, we say that the general coordinate transformations (or diffeomorphisms) on a manifold are the gauge transformations of the theory. The local Lorentz transformations are the orthogonal rotations in the tensor bundle of the manifold. Thus the structure group of the fibre bundle is essentially the Lorentz group (for manifold with a Lorentzian metric).

Now the structure group is a set of transformations which essentially performs rotations in the bundle which, means it changes the basis in a specific way. And in cases where we use natural basis (coordinate basis), it should mean just changing the coordinates. But that is essentially a diffeomorphism (which is gauge transformation). But Lorentz symmetry cannot be a gauge symmetry. So I was wondering where I am going wrong.

On another note, I wonder if GR is a gauge theory in typical sense. Generally, the structure group in the fibre bundle of a manifold, in a gauge theory, forms a gauge group. But for GR, the structure group of the fibre bundle is giving the actuall symmetries of the theory (Lorentz transformations).

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# A LLT, GCT and gauge transformations

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