Question

What is wrong in following arguments about connection of local gauge invariance and causality?

Answer 1

"...The most theories of free fields are invariant under global gauge transformations. It can be interpreted as instantaneous "rotation" of all space-time relatively gauge space, which contradicts the causality (of gauge transformations) in relativity case, because the speed of interactions is limited by according to it. So we introduce local gauge transformations, where "rotation" depends on space-time point. The gauge states is indistinguishable in a case of free field. But when our global gauge invariance field interacts with other fields, degeneracy is lifted, and this leads to instant changes in interaction. Thus we satisfy causality principle for gauge transformations.

Answer 2

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✔️✔️ Arguments about connection of local gauge invariance and causality

So we introduce local gauge transformations, where "rotation" depends on space-time point. The gauge states is indistinguishable in a case of free field.

But when our global gauge invariance field interacts with other fields, degeneracy is lifted, and this leads to instant changes in interaction.

Thus we satisfy causality principle for gauge transformations.

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