Baryon density of quarks coupled to a chiral field

Abstract

We calculate orbitals for quarks coupled to a chiral field with a hedgehog shape, as well as the baryon density in the one-loop approximation. Under certain conditions, the baryon density is found to be very similar to that of a skyrmion. An extra quark orbital enters the Dirac sea each time the winding number of the chiral field increases by one unit thereby providing a mechanism which allows one to identify the windling number with the baryon number.