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This is a consequence ofPCT invariance (1).
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Sartori, G. Constraints on equal-time commutators from lorentz covariance. Lettere Nuovo Cimento (1969-1970) 4, 583–588 (1970). https://doi.org/10.1007/BF02755319
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DOI: https://doi.org/10.1007/BF02755319