# Negative probability and spin-0 scalar field in Klein-Gordon equation

Klein-Gordon equation in quantum field theory is known to suffer from the possibility of negative probability. So, the question is, despite this, Klein-Gordon describes spin-zero field. So, how can negative probability and scalar field co-exist?

• I thought the Dirac density $j^{0} = \bar{\psi} \gamma^{0} \psi$ was positive definite... what do you mean by "The Dirac equation also has this property"? – P. C. Spaniel Feb 12 '17 at 22:22
• @Spaniel: This issue is "circumvented" or fixed when the solutions of the Dirac equation are promoted to field-operators with anti-commutator rules. In that case if $j^0$ (as operator) is applied on a anti-particle state, is gets an negative eigenvalue, whereas applied on particle states, the eigenvalue is positive. – Frederic Thomas Sep 11 '17 at 17:48