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Gauge transformations are changes to the fields in a physical theory that do not alter the observable quantities or the physical predictions of the theory. In electromagnetism, for example, a gauge transformation modifies the electric and magnetic potentials without affecting the electric and magnetic fields themselves. This reflects the underlying symmetry of the theory and emphasizes that certain mathematical descriptions do not correspond to physical differences. Gauge invariance is fundamental in ensuring the consistency and renormalizability of quantum field theories.

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