4 Vacuum effects in electrodynamics and in Yang - Mills theory in ( 2 + 1 ) dimensions

Vacuum effects in (2+1)-dimensional quantum electrodynamics (QED) with the topological Chern-Simons term are considered. The photon polarization operator is studied and the decay rate for the electron-positron photoproduction γ → e+ e− is presented as a function of the photon energy and external field strength. The radiatively induced electron mass shift in an external magnetic field is investigated both taking the topological Chern-Simons term into account and ignoring it. Moreover, the electron self-energy in topologically massive (2+1)-QED at finite temperature and density is studied. Finally, the parity breaking part of the action in the framework of the SU(2)×U(1) gauge field model at finite temperature is considered. The massive fermion contribution to the one-loop effective action in the background of the superposition of an abelian and a nonabelian gauge fields leading to parity breaking in the finite temperature (2+1)-quantum field theory is discussed.