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Multiple choice
Dirac sought a relativistic wave equation that is FIRST order in the time derivative. For the resulting Dirac equation, what is the time component of the conserved current
j
0
=
ρ
j^0 = \rho
j
0
=
ρ
, and what desirable property does it have?
ρ
=
ψ
†
ψ
\rho = \psi^\dagger \psi
ρ
=
ψ
†
ψ
but it can take negative values for negative-energy solutions
ρ
\rho
ρ
equals the energy
E
E
E
, which is negative for half the solutions
ρ
=
ψ
†
ψ
=
∑
∣
ψ
a
∣
2
\rho = \psi^\dagger \psi = \sum |\psi_a|^2
ρ
=
ψ
†
ψ
=
∑
∣
ψ
a
∣
2
over the four components, which is manifestly non-negative (
≥
0
\geq 0
≥
0
)
ρ
\rho
ρ
involves a first time derivative of
ψ
\psi
ψ
and can be negative, just as in Klein-Gordon
Check answer