Baglike solutions of a Dirac equation with fractional nonlinearity

Numerical solutions are obtained for a classical spinor equation derived from the Dirac Lagrangian augmented by the self-interacting term $-b{\left|\overline{\psi }\psi \right|}^{a-1\mathrm{}}\overline{\psi }\psi$, $0<a<\mathrm{}1\mathrm{}$. The finite-energy stationary states are found to be exactly zero outside a finite domain. They are examples of nontopological solitons. The energy-charge curve is shown to be everywhere concave, which implies stability with respect to fission into other stationary solitons. The MIT bag model is recovered as a limiting case $a\to 0$; in this case, the self-coupling constant $b$ is identified with the bag pressure.