Sorry my last entry should have had the first Dirac eq as the adjoint $$ψ^* γ^0 γ^0 ψ $$
I redid the idea of is real(Dirac eq #1) <> real(Dirac eq 1 to 4) a million times with random choices for the complex (about 1 to 0) $$ψ^μ$$ and the real part of the first Dirac eq is always larger than...
Thanks. I checked on the adjoint point. Adjoint means the conjugate transpose. I'm trying to use some curve fitting on the ψ's and this leads to problems. Such as the four terms in $$ψ^t γ^0 γ^0 ψ$$ would all ways be positive and this would make the first Dirac current always larger than the...
I'm having a problem writing the third Dirac current eq.
$$1 = \int ψ^t \gamma^0 \gamma^2 ψ$$
which should come out as
$$1 = \int i ψ^0 ψ^3 - i ψ^1 ψ^2 + i ψ^2 ψ^1 - i ψ^3 ψ^0$$
By inspection the first and last terms add to zero and the second and third terms add to zero, so the integral...