The spontaneous generation of magnetic and chromomagnetic fields at high temperature in the standard model

The spontaneous generation of magnetic and chromomagnetic fields at high temperature is investigated in the standard model. The consistent effective potential including the one-loop and the daisy diagrams of all boson and fermion fields is calculated. The mixing of the generated fields due to the quark loop diagram is studied in detail. It is found that the quark contribution increases the magnetic and chromomagnetic field strengths as compared with the separate generation of fields. The magnetized vacuum state is stable due to the magnetic gauge field masses included in the daisy diagrams. Some applications of the results obtained are discussed. Received: 25 October 2001 / Published online: 26 July 2002