Fock and Ivanenko (1929) demonstrated explicitly that Dirac's equation admits generally covariant formulation using this extended calculus, empirically refuting the claim that tensor methods are categorically improper.
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A way of writing an equation so it works the same way no matter what coordinate system or reference frame you use—important for relativity because the laws of physics should be the same everywhere.
Tensor methods(as the questioned mathematical approach)
Mathematical techniques using objects called tensors—a way of organizing and manipulating numbers that helps describe how things change across different directions and spaces.