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We define pseudoperturbations as the difference between two Hamiltonians that are related by a generalized gauge transformation. We state and prove the theorem that such pseudoperturbations cannot cause any real physical transitions. We also rigorously establish the generalized gauge invariance of physical transition-matrix elements in real processes. Our theorem also generates some interesting sum rules and onshell identities which can serve as useful constraints in variational calculations.
Aharonov et al. (Mon,) studied this question.