The violation of the Bell inequality for Dirac fermions is investigated in the cosmological de Sitter spacetime, in the presence of background electromagnetic fields of constant strengths. The orthonormal Dirac mode functions are obtained and the relevant in-out squeezed state expansion in terms of the Bogoliubov coefficients are found. We focus on two scenarios here : strong electric field and heavy mass limits (with respect to the Hubble constant). Using the squeezed state expansion, we then demonstrate the Bell violations for the vacuum and some maximally entangled initial states. Even though a background magnetic field alone cannot create particles, in the presence of background electric field and or spacetime curvature, it can affect the particle creation rate. Our chief aim thus here is to investigate the role of the background magnetic field strength in the Bell violation. Qualitative differences in this regard for different maximally entangled initial states are shown. Further extension of these results to the so called α-vacua are also discussed.

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We have studied the decoherence mechanism in a fermion and scalar quantum field theory with the Yukawa interaction in the Minkowski spacetime, using the non-equilibrium effective field theory formalism appropriate for open systems. The scalar field is treated as the system whereas the fermions as the environment. As the simplest realistic scenario, we assume that an observer measures only the Gaussian 2-point correlator for the scalar field. The cause of decoherence and the subsequent entropy generation is the ignorance of information stored in higher-order correlators, Gaussian and non-Gaussian, of the system and the surrounding. Using the 2-loop 2-particle irreducible effective action, we construct the renormalised Kadanoff–Baym equation, i.e., the equation of motion satisfied by the 2-point correlators in the Schwinger–Keldysh formalism. These equations contain the non-local self-energy corrections. We then compute the statistical propagator in terms of the 2-point functions. Using the relationship of the statistical propagator with the phase space area, we next compute the von Neumann entropy, as a measure of the decoherence or effective loss of information for the system. We have obtained the variation of the entropy with respect to various relevant parameters. We also discuss the qualitative similarities and differences of our results with the scenario when both the system and the environment are scalar fields.

In this article, we have solved the Dirac equation explicitly and performed the field quantization in the Rindler spacetime in the presence of background electromagnetic fields of constant strengths, and in and out modes are computed. We next consider the full Rindler right and left wedges and construct the local and global modes and their Bogoliubov transformations. Using the squeezed state expansion obtained from the Bogoliubov transformation, the spectra of created particles are computed. We also discuss some applications of this result in the context of quantum entanglement. We forge on the interpretation of pair creation in the Rindler spacetime with background electromagnetic fields of constant strengths. Our chief motivation is that the astrophysical black holes are often endowed with such background fields due to the accretion of plasma. The model considers here serves as a very simple toy model to address such a scenario.

This paper aims to discuss the numerical investigations of the equatorial lensing (θ = π/2) by a recently obtained exact rotating black holes solution in EiBI theory in both the strong and weak field limit. The black hole is a modification to the Kerr-Newman black holes of general relativity in EiBI gravity. There appears an extra new term as a correction to GR, in addition to its mass (M ), the charge (Q), and the rotation parameter (a). We show numerically the variations of the impact parameter u m , the light deflection coefficients p and q, the total azimuthal bending angle α D and find a close dependence of these quantities on the charge parameter r q , the correction term and the spin a. We also calculate the angular position θ ∞ , and the angular separation s, and the magnification of the relativistic images. In addition, we also discuss the weak lensing the black holes in EiBI theory using the Gauss-Bonnet theorem. We calculate the weak lensing parameter and find its variation with different values of the parameters r q and .