Baryon number nonconservation in extreme conditions

In gauge theories with the left-right asymmetric fermionic content (e.g. in standard electroweak theory) fermion number F is not conserved due to the anomaly. It is shown that anomalous processes, while being exponentially suppressed, under normal conditions, are in fact rapid. The mechanism of fermionic number nonconservation connected with a level crossing phenomenon in external gauge fields is described. The theory and experimental consequences of monopole catalysis of a proton decay is reviewed. It is shown that cold dense fermionic matter is stable only up to some limiting density. It is demonstrated that there is no exponential suppression of the rate F nonconservation at high temperatures. The cosmological implications of this fact are discussed. The strong anomalous fermionic number violation in decays of superheavy fermions technibaryons is considered