Vacuum Polarization Effects in the Background of Nontrivial Topology
- 746 Downloads
Topological phenomena are of great interest and importance because of their universal nature connected with general properties of space-time, on the one hand, and their numerous practical aspects, on the other hand. Since the discovery of Bohm and Aharonov 40 years ago, it has become clear that topology has to do with the fundamental principles of quantum theory. At present much attention is paid to the study of nonperturbative effects in quantum systems, arising as a consequence of interaction of quantized fields with a topologically nontrivial classical field background. The dependence of the vacuum polarization effects on the geometry and topology of the base space was discovered by the present author 9 years ago. In particular, it was shown that there exists a field-theoretical analogue of the Bohm-Aharonov effect: singular configurations of the external magnetic field strength induce vacuum charge on noncompact topologically nontrivial surfaces even in cases when the magnetic flux through such surfaces vanishes. This is due to the fact that in some noncompact, essentially curved or topologically nontrivial, spaces the asymptotics of the axial-vector current becomes nontrivial and contributes to the induced vacuum charge. As a result, the latter depends on global geometric characteristics of space, as well as on global characteristics of external field strength (total anomaly).