Critical Couplings in the Nambu--Jona-Lasinio Model with the Constant Electromagnetic Fields

摘要

A detailed analysis is performed for the Nambu--Jona-Lasinio model coupledwith constant (external) magnetic and/or electric fields in two, three, andfour dimensions. The infrared cut-off is essential for a well-definedfunctional determinant by means of the proper time method. Contrary to theprevious observation, the critical coupling remains nonzero even in threedimensions. It is also found that the asymptotic expansion has an excellentmatching with the exact value.