Fractional charge definitions and conditions

Fractional charge is known through theoretical and experimental discoveries of isolable objects carrying fractions of familiar charge units { electric charge Q, spin S, and the dierence of baryon and lepton numbers B-L. With a few simple assumptions all these eects may be described using a generalized version of charge renormalization for locally conserved charges, in which medium correlations yield familiar adiabatic, continuous renormalization, or sometimes nonadiabatic, discrete renormalization. Fractional charges may be carried by fundamental particles or fundamental solitons. Either picture works for the simplest fractional-quantum-Hall-eect quasiholes, though the particle description is far more general. The only known fundamental solitons in three or fewer space dimensions d are the kink (d = 1), the vortex (d = 2), and the magnetic monopole (d = 3). Further, for a charge not intrinsically coupled to the topological charge of a soliton, only the kink and the monopole may carry fractional values. The same reasoning enforces fractional values of B-L for electrically charged elementary particles. (J. Math. Phys. 44, 3607 (2003), corrected and sharpened)