Efeitos induzidos por uma corda cósmica na dinâmica relativística e na polarização do vácuo de campos de matéria - Medeiros, Eduardo Rafael Figueiredo (2014)
In this thesis, we investigate quantum properties associated with massive fields near a cosmic string within two distinct scenarios: a Minkowski flat background, and a maximally symmetric anti-de Sitter spacetime (AdS). Initially, we present a brief review of the formalism needed in our contribution. In Minkowski spacetime, we analyze the relativistic quantum dynamics of bosonic and fermionic charged particles in the presence of a magnetic field also considering the presence of scalar potentials. In order to develop this analysis, we assume that the magnetic field is parallel to the string axis, and the scalar potentials present a cylindrical symmetry with their center on the string. Two distinct configurations for the scalar potential are considered: (i) the potential proportional to the inverse of the polar distance, and (ii) the potential linearly proportional to this distance. The energy spectra are explicitly computed for different physical situations, and their dependence on the magnetic field strength, and scalar coupling constants are presented. In the context of a string in AdS, we investigate the quantum properties of a massive fermionic field. More specifically, we calculate the fermionic condensate (FC), (4RP), and the vacuum expectation value (VEV) of the energy-momentum tensor, (T"), induced by the presence of a cosmic string. In order to develop this analysis, we consider the MIT bag boundary condition on the boundary of AdS. The FC and the VEV of the energy-momentum tensor are decomposed into pure AdS and cosmic string induced parts. The string-induced part in the VEV of the energy-momentum tensor is diagonal, and the axial, and radial stresses are equal to the energy density. For points near the cosmic string, the effects of the curvature are sub-dominant and to leading order, the VEVs coincide with the corresponding VEVs for the cosmic string in the Minkowski bulk. At large proper distances from the string, the decay of the VEVs show a power-law dependence on the distance for both massless and massive fields, in contrast to the case of a Minkowski bulk where, for a massive field, the string-induced parts decay exponentially.