= Indefinite Klein-Gordon charge density
For a complex <Klein-Gordon field>, $j^\mu=i(\phi^*\partial^\mu\phi-\phi\partial^\mu\phi^*)$ is conserved. A mode $\phi=N e^{-iEt+i\mathbf p\cdot\mathbf x}$ has $j^0=2E|N|^2$, so unrestricted positive- and negative-frequency solutions do not have a positive probability norm under this current. In the quantized complex field, the associated conserved quantity is charge: particles and <antiparticles> contribute with opposite signs while both have positive excitation energy and positive <Fock space> norm.
Back to article page
