We investigated the effects of the global monopole spacetime on the Dirac and Klein–Gordon relativistic quantum oscillators. In order to do this, we solve the Dirac and Klein–Gordon equations analytically and discuss the influence of this background, which is characterised by the curvature of the spacetime, on the energy profiles of these oscillators. In addition, we introduce a hard-wall potential and, for a particular case, determine the energy spectrum for relativistic quantum oscillators in this background.

In this paper we review some important aspects of the global monopole spacetime and present how this manifold modifies, at classical and quantum points of view, the movement of a charged particle. The explicit calculations of the renormalized vacuum expectation values of the energy-momentum tensors, áTmn(x)ñRen., associated with massless bosonic and fermionic fields are also presented. Moreover the effect of the nonzero temperature in this previous formalism is analyzed. Finally, we briefly present other applications of this manifold in the topological inflation and condensed matter system.

In this paper, we consider a Lorentz-breaking extension of the theory for a real massive scalar quantum field in the region between two large parallel plates, with our manner to break the Lorentz symmetry being $CPT$ even and aetherlike. For this system, we calculated the Casimir energy considering different boundary conditions. It turns out that the Casimir energy strongly depends on the direction of the constant vector implementing the Lorentz symmetry breaking as well as on the boundary conditions.

We evaluate the Hadamard function and the vacuum expectation value of the current density for a massive complex scalar field in the generalized geometry of a straight cosmic string with a finite core enclosing an arbitrary distributed magnetic flux along the string axis. For the interior geometry, a general cylindrically symmetric static metric tensor is used with finite support. In the region outside the core, both the Hadamard function and the current density are decomposed into the idealized zero-thickness cosmic string and core-induced contributions. The only nonzero component corresponds to the azimuthal current. The zero-thickness part of the latter is a periodic function of the magnetic flux inside the core, with the period equal to the quantum flux. As a consequence of the direct interaction of the quantum field with the magnetic field inside the penetrable core, the core-induced contribution, in general, is not a periodic function of the flux. In addition, the vacuum current, in general, is not a monotonic function of the distance from the string and may change the sign. For a general model of the core interior, we also evaluate the magnetic fields generated by the vacuum current. As applications of the general results, we have considered an impenetrable core modeled by Robin boundary condition, a core with the Minkowski-like interior and a core with a constant positive curvature space. Various exactly solvable distributions of the magnetic flux are discussed.

We investigate the vacuum expectation value of the fermionic current induced by a magnetic flux in a (2+1)-dimensional conical spacetime in the presence of a circular boundary. On the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, a special case of boundary conditions at the cone apex is considered, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. We observe that the vacuum expectation values for both the charge density and azimuthal current are periodic functions of the magnetic flux with the period equal to the flux quantum whereas the expectation value of the radial component vanishes. For both exterior and interior regions, the expectation values of the current are decomposed into boundary-free and boundary-induced parts. For a massless field the boundary-free part in the vacuum expectation value of the charge density vanishes, whereas the presence of the boundary induces nonzero charge density. Two integral representations are given for the boundary-free part in the case of a massive fermionic field for arbitrary values of the opening angle of the cone and magnetic flux. The behavior of the induced fermionic current is investigated in various asymptotic regions of the parameters. At distances from the boundary larger than the Compton wavelength of the fermion particle, the vacuum expectation values decay exponentially with the decay rate depending on the opening angle of the cone. We make a comparison with the results already known from the literature for some particular cases.