Abstract
The proper-time Schwinger formalism is implemented in a derivation of the gap equation and total energy of a system of interacting fermions described by the Nambu–Jona-Lasinio model that is minimally coupled to a constant electromagnetic field. Inclusion of a Lagrange multiplier term to vary the scalar density enables the calculation of energy curves as a function of the scalar density that plays the role of an order parameter. A consistent gauge- and Lorentz-invariant regularization of the divergent quantities that occur in this theory is implemented in calculating the total energy and gap relation. Specializing to constant electric fields, we find that a chiral-symmetry-restoration phase transition can occur at a critical value of the electric field. For our choice of parameters, g/2=1.12 and Λ=1041 MeV, one finds the dynamically generated mass =208 MeV and critical field =(270 MeV. By contrast, a constant magnetic field is found to inhibit the phase transition by stabilizing the chirally broken vacuum state.
- Received 29 September 1988
DOI:https://doi.org/10.1103/PhysRevD.39.3478
©1989 American Physical Society