Charge fluctuations and fractional charge of fermions in 1 + 1 dimensions

Charge fluctuations of solitons with arbitrary fractional fermion number in 1 + 1 dimensions are calculated, generalizing the result of Kivelson and Schrieffer for solitons with fermion number 1/2. The soliton charge is measured by a sampling function f(x) such that f(x)1 over a region of width L around the soliton and then falls to zero in a distance l. It is shown that vacuum fluctuations vanish as l-1 for large l while the additional fluctuations due to the presence of a soliton vanish as either exp(-Lξ) or exp(-2Δ0L); ξ is the soliton width and Δ0 is the mass gap of a ground state. This result establishes that the fractional fermion charge is a well-defined observable.