Please help me to understand the following situation.
A fermion field $\Psi(x)$ acting on the vacuum can destroy a particle and create an antiparticle. If however, a chiral field $\Psi_L$ defined as $\Psi_L=\frac{1-\gamma_5}{2}\Psi$ acts on the vacuum, how does one argue that it creates a right-handed antiparticle. Please help me to show this.
