A Dyson-Schwinger calculation shows that in a magnetic field, quarks acquire distinct transverse and longitudinal effective masses, with the transverse mass always larger, and a mass splitting that grows roughly as the 1.5-1.8 power of the field strength.
Gauge independent approach to chiral symmetry breaking in a strong magnetic field
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abstract
The gauge independence of the dynamical fermion mass generated through chiral symmetry breaking in QED in a strong, constant external magnetic field is critically examined. We show that the bare vertex approximation, in which the vertex corrections are ignored, is a consistent truncation of the Schwinger-Dyson equations in the lowest Landau level approximation. The dynamical fermion mass, obtained as the solution of the truncated Schwinger-Dyson equations evaluated on the fermion mass shell, is shown to be manifestly gauge independent. By establishing a direct correspondence between the truncated Schwinger-Dyson equations and the 2PI (two-particle-irreducible) effective action truncated at the lowest nontrivial order in the loop expansion as well as in the 1/N_f expansion (N_f is the number of fermion flavors), we argue that in a strong magnetic field the dynamical fermion mass can be reliably calculated in the bare vertex approximation.
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Anisotropic quark propagation and Zeeman effect in an external magnetic field
A Dyson-Schwinger calculation shows that in a magnetic field, quarks acquire distinct transverse and longitudinal effective masses, with the transverse mass always larger, and a mass splitting that grows roughly as the 1.5-1.8 power of the field strength.