Flutuações quânticas e ação efetiva em teoria semiclássica

Abstract

In this thesis, two different works are included. First, we study the conformal anomaly in a curved space-time with antisymmetric torsion. Furthermore, we also analyzed the effects of quantum fluctuations of an electromagnetic field on the motion of a particle with zero charge but nonzero dipole moment that interacts with the field in the presence of a perfectly conducting boundary in finite temperature regime. First, we review some properties of semiclassical gravitation in a curved space-time with torsion, where we present how torsion interacts with matter fields. We then studied the effective action in the presence of torsion, where we used two different conjugate operators for the fermionic case, making it possible to recover results presented in the literature and still generalize them, obtaining a new type of ambiguity that we relate with a new example of multiplicative anomaly. We also calculated the anomaly-induced action in its covariant form, obtaining local and non-local terms, where the local term has the ambiguity due to the multiplicative anomaly, and it was possible to rewrite the non-local term using two auxiliary fields to obtain also its local form. Next, we perform the quantization of the electromagnetic field in the presence of an ideally reflecting flat boundary in a finite temperature scenario. And finally, on the behavior of the dipole, we saw that its interaction with the fluctuations of the electromagnetic field produced quantum dispersions of the linear and angular momenta, whose magnitudes depend on the temperature, distance to the wall and also on the characteristics of the dipole moment. We also analyze the kinetic energy acquired by the dipole, studying its different contributions separately, where we show that, when the particle experiences only the thermal bath or the conducting boundary, its residual energy is positive.