If the proper criterion for mathematical instruments is empirical adequacy rather than transformation-group universality, then any calculus yielding generally covariant Dirac equations satisfies the requirement, regardless of its affine limitations.
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A mathematical property where equations remain valid (look the same) when you change your coordinate system or perspective—a sign of deep mathematical elegance and unity.
criterion(as used in philosophy to describe a test for whether an idea works)
A standard or rule used to decide whether something counts as true or valid.
empirical adequacy(Distinguished from full accuracy in that the degree of accuracy required depends on pragmatic considerations)
The requirement that theories account for observations; a constraint that all legitimate research programs must satisfy