How to think about antiparticles in KG equation?

Question

I am a beginner to study QFT and have a problem.

I know, in Dirac equation, thanking to the Pauli exclusion principle and believing that the vacuume is the state that all the negative energy states are occupied and all the positive energy states are empty, the antiparticles in Dirac equation are not occupied negative energy states, the positons just like holes in occupied states.

But in the KG equation, a equation for zero spin particles, there is not Pauli exclusion priciple and it is not a good idea that think the vacuume is the same as the case in Dirac equation because particles will jump from positive energy states to negative energy states and successively jump to the lower energy states.

So, how to explain the antiparticles in KG equation?

Answer 1

The Dirac sea concept is only the particular case of consequence of the postulate of existence only positive energies free particles (fields). Let's talk about application of this postulate in general.

According to it, we build the expression for the operators of energy, impulse and charge (Noether current) of free particles (field). It is expressed in terms of creation/destruction operators $\hat {a}, \hat {a}^{+}, \hat {b}, \hat {b}^{+}$. Then we look to the sign of the energy and momentum operators eigenvalues and then impose commutation or anticommutation relatives for creation/destruction operators for the absense of negative eigenvalues (for talking about sign of eigenvalue we need to determine the vacuum state $| \rangle$ of the system particles as $\hat {a}| \rangle = \hat {b} | \rangle = 0$). This automatically implies that impulse, energy and charge operators have common basis, and in a case of the complex field acting by the charge operator on the one-particle state $\hat {a}^{+}| \rangle$ leads to $-\hat {a}^{+}| \rangle$, and for the case $\hat {b}^{+}$ it leads to $\hat {b}^{+}| \rangle$. So we say that $\hat {a}^{+}| \rangle$-state has negative charge, and $\hat {b}^{+}| \rangle$-state has positive charge, while both of them have positive energy values.