Narrow Results

The reduction formulas for Dirac fermions is derived using the exact solutions of free Dirac equation on de Sitter space–time. In the framework of the perturbation theory one studies the Green functions and derives the scattering amplitude in the first orders of perturbation theory.

We study the theory of interaction between charged scalar field and Maxwell field in de Sitter background. Solving the equation of interacting fields, we define the in–out fields as asymptotic free fields and construct the reduction formalism for scalar field. Then we derive the perturbation expansion of the scattering operator. The first-order transition amplitudes corresponding to particle production from de Sitter vacuum and pair production in an external field are analyzed. We show that all these effects are important only in strong gravitational fields and vanish in the flat limit.

We study the localization properties of fundamental fields which are coupled to one another through the gauge mechanism both in the original Randall–Sundrum (RS) and in the modified Randall–Sundrum (MRS) braneworld models: scalar–vector, vector–vector, and spinor–vector configuration systems. For this purpose, we derive conditions of localization, namely, the finiteness of integrals over the extra coordinate in the action of the system considered. We also derive field equations for each of the systems and then obtain their solutions corresponding to the extra dimension by a separation of variable method for every field involved in each system. We then insert the obtained solutions into the conditions of localization to seek whether or not the solutions are in accordance with the conditions of localization. We obtain that not all of the configuration systems considered are localizable on the brane of the original RS model while, on the contrary, they are localizable on the MRS braneworld model with some restrictions. In terms of field localizability on the brane, this result shows that the MRS model is much better than the original RS model.

We will present the axioms of Bogoliubov’s causal perturbative QFT in which the creation-annihilation operators are interpreted as Hida operators. We will shortly present the results that can be achieved in this theory: (1) removal of UV and IR infinity in the scattering operator, (2) existence of the adiabatic limit for interacting fields in QED, (3) proof that charged particles have nonzero mass, (4) existence of infrared and ultraviolet asymptotics for QED.

In this paper, the vacuum energy density and generation of topological mass are investigated for a system of a real and complex scalar fields interacting with each other. In addition to that, it is also included the quartic self-interaction for each one of the fields. The condition imposed on the real field is the periodic condition, while the complex field obey a quasi-periodic condition. The system is placed in a scenario where the CPT-even aether-type Lorentz symmetry violation takes place. We allow that the Lorentz violation affects the fields with different intensities. The vacuum energy density, its loop correction, and the topological mass are evaluated analytically. It is also discussed the possibility of different vacuum states and their corresponding stability requirements, which depends on the conditions imposed on the fields, the interaction coupling constants and also the Lorentz violation parameters. The formalism used here to perform this investigation is the effective potential one, which is written as a loop expansion via path integral in quantum field theory.