Fractional fermion number in a(1+1)-dimensional Dirac equation with a scalar Coulomb field

Abstract

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 $\ifmmode\pm\else\textpm\fi{}1/2$ depending on whether the lowest positive energy state without the external scalar field was filled or empty.