Summary
In spite of the fact that pure gauge transformations (in the general sense of Levy-Leblond) can change the functional form of the Dirac brackets, the whole scheme of Dirac mechanics and the corresponding canonical quantization, remain gauge invariant.
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Tello-Llanos, R.A. Gauge invariance of Dirac’s generalized mechanics. Lett. Nuovo Cimento 40, 115–120 (1984). https://doi.org/10.1007/BF02747085
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DOI: https://doi.org/10.1007/BF02747085