An elementary example of fermion number fractionalization is given. The model considered is a massive Dirac fermion moving on the positive halfline in an external scalar Coulomb field. The theory is symmetric under charge conjugation. We demonstrate the existence of a nondegenerate, normalizable, and self-charge-conjugate zero energy solution in the theory. The vacuum thus has a fermion number ±1/2 depending on whether the lowest positive energy state without the external scalar field was filled or empty.
Physical Review D (Particles and Fields) 63(2), 27701(2pages)