Polarization of the magnetized scalar and spinor vacua

Abstract

The vacuum polarization tensor of the magnetized boson system, taken within the random phase or one-loop approximation, is presented in three representation forms: the Landau, the proper-time, and the dispersion sum representation. Detailed numerical investigations into many aspects of the physical properties of both the bosonic and fermionic vacua are presented on the basis of these analytical results. From the static and uniform limit of the polarization scalars it is found that the boson vacuum state enhances small electrostatic fields parallel to the external field as well in the transverse direction contrary to the screening behaviour of the fermion vacuum, and all scalars have a weak logarithmic growth in strong fields. Also contrary to the fermionic behaviour, for wavevectors parallel to the field, the longitudinal dielectric function does not exhibit any singularities at the pair production thresholds. Furthermore the 'massive longitudinal photon' mode found for the magnetized fermion vacuum does not exist in the bosonic equivalent. Like the spin-1/2 case the dispersion solutions show that the purely transverse 'photon' mode (3) acquires mass and is channelled along the field lines, thus manifesting the mixed state of a photon and a boson-antiboson quasibound state. However, the other mode (2), which is a combined longitudinal-transverse mode does not deviate significantly from the free-space dispersion law and its inverse lifetime has no singularities at the pair threshold.