Motivation
The Dirac adjoint is motivated by the need to form well-behaved, measurable quantities out of Dirac spinors. For example, is not a Lorentz scalar, and is not even Hermitian. One source of trouble is that if is the spinor representation of a Lorentz transformation, so that
then
Since the Lorentz group of special relativity is not compact, will not be unitary, so . Using fixes this problem, in that it transforms as
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