ABSTRACT
The form of the effective action determines quantum phenomena as axial, conformai and gravitational anomalies, quantum corrections to Einstein equations and curvature induced phase transitions. This chapter discusses curvature induced phase transitions in gauge theories in curved space-time. It considers the problem of the calculation of asymptotics of the effective action in strong fields. The chapter also considers a cosmological model in gravity with torsion on the basis of the effective action caused by vacuum quantum effects. It describes quantum fields in an external gravitational field with torsion and examines the one-loop corrections to the external-field action. Within the renormalization group method, the chapter deals with the multiplicatively renormalized theories. The renormalization group equations lead directly to finding the effective potential in curved space. It also deals with the investigation of the asymptotics of ea and with the question of stability of the quantum field theory in curved space-time.
