On the behavior of symmetry and phase transitions in a strong electromagnetic field

Symmetry behavior and phase transitions in a strong electromagnetic field are investigated by using the one-loop effective potential. The one-loop effective potential in a uniform external field is constructed by virtue of the ζ-function regularization method and general discussions are given concerning the symmetry behavior in the strong electromagnetic field by using it. It is emphasized that nonperturbative effects about the field strength are essential in the strong electromagnetic field and they qualitatively modify the results obtained by using the perturbative formula. Furthermore, even qualitative differences between fermion and scalar contributions are seen in the strong electromagnetic field, although no qualitative differences are seen at finite temperatures. Subsequently, two typical subjects are discussed within this approach; the chiral phase transition in the linear σ-model and the vanishing of the Cabibbo angle in a toy model. It is found that in both cases, the electric field restores the symmetry, while the magnetic field breaks it further; the critical electric field of the chiral phase transition is eE c ⋍ (480 MeV) 2 when the magnetic field is absent, H = 3. The characteristic field strengths for the Cabibbo-angle problem are H ∗ ⋍ 1.5 × 10 19 G and E ∗ ⋍ 5 × 10 18 G .