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In this paper, I investigate the effect of a magnetic field on the Casimir effect due to a massless and charged fermion field that violates Lorentz invariance according to the Horava-Lifshitz theory. I focus on the case of a fermion field that obeys MIT bag boundary conditions on a pair of parallel plates. I carry out this investigation using the ζ -function technique that allows me to obtain Casimir energy and pressure in the presence of a uniform magnetic field orthogonal to the plates. I investigate the cases of the parameter associated with the violation of Lorentz invariance being even or odd and the cases of weak and strong magnetic field, examining all possible combinations of the above quantities. In all cases I obtain simple and very accurate analytic expressions of the magnetic field-dependent Casimir energy and pressure. [ABSTRACT FROM AUTHOR]

In this paper, a model of a pulsating universe is investigated with periodic function of the scale factor together with a homogeneous, isotropic and spatially flat Friedman-Robertson-Walker metric. The parameters of the pulsating universe model coincide with observation parameters of the modern universe, taking into account the different contributions of various types of matter to its evolution. In the resulting solution, during periods of accelerated expansion of the universe, the scalar field with negative pressure makes a greater contribution to the expansion growth. The fermionic field and the vector field, which have positive pressure values during this period, prevent the growth of this expansion. During periods of compression, the fermionic field and the vector field have a greater influence on the dynamics of the evolution of the universe. In the resulting periodic solution, the universe goes through endless cycles of expansion and contraction. The observed modern accelerated expansion of the universe corresponds to one of these cycles. Cosmographic parameters are calculated - parameters of deceleration q, jerk j and snap s and energy conditions for the model under research. These parameters make it possible to link model-independent results obtained from cosmography with theoretically sound assumptions of gravity. [ABSTRACT FROM AUTHOR]

In this work, we investigate a cosmological model with the tachyon and fermion fields with barotropic equation of state, where pressure p , energy density ρ and barotropic index γ are related by the relation p = (γ − 1) ρ. We applied the tachyonization method which allows to consider cosmological model with the fermion and the tachyon fields, driven by special potential. In this paper, tachyonization model was defined from the stability analysis and exact solution standard of the tachyon field. Analysis of the solution via statefinder parameters illustrated that our model in fiducial points with deceleration parameter q = 0. 5 and statefinder r = 1 corresponds to the matter-dominated universe (SCDM) but ends its evolution at a point in the future (q = − 1 , r = 1) which corresponds to the de Sitter expansion. Comparison of the model parameters with the cosmological observation data demonstrates that our proposed cosmological model is stable at barotropic index γ 0 = 0. 0 0 7 4 4. [ABSTRACT FROM AUTHOR]

Abstract This work deals with fermions in the background of distinct localized structures in the two-dimensional spacetime. Although the structures have a similar topological character, which is responsible for the appearance of fractionally charged excitations, we want to investigate how the geometric deformations that appear in the localized structures contribute to the change in the physical properties of the fermionic bound states. We investigate the two-kink and compact kinklike backgrounds, and we consider two distinct boson–fermion interactions, one motivated by supersymmetry and the other described by the standard Yukawa coupling.

The Schwinger–de Witt and Hadamard methods are used to obtain renormalised vacuum expectation values for the fermion condensate, charge current and stress-energy tensor of a quantum fermion field of arbitrary mass on four-dimensional anti-de Sitter space–time. The quantum field is in the global anti-de Sitter vacuum state. The results are compared with those obtained using the Pauli–Villars and zeta-function regularisation methods, respectively.

This paper examines the interaction of an intense fermion field with all of the particle species of an attometer primordial black hole's (PBH) high energy Hawking radiation spectrum. By extrapolating to Planck-sized PBHs, it is shown that although Planck-sized PBHs closely simulate the zero absorption requirement of white holes, the absorption probability is not truly zero, and therefore, thermodynamically, Planck-sized primordial black holes are not true white holes. [ABSTRACT FROM AUTHOR]

The Schwinger–de Witt and Hadamard methods are used to obtain renormalised vacuum expectation values for the fermion condensate, charge current and stress-energy tensor of a quantum fermion field of arbitrary mass on four-dimensional anti-de Sitter space–time. The quantum field is in the global anti-de Sitter vacuum state. The results are compared with those obtained using the Pauli–Villars and zeta-function regularisation methods, respectively. [ABSTRACT FROM AUTHOR]

We show that the Wightman function of a free quantum field generates any complete set of solutions of the relativistic wave equations. Using this approach, we construct the complete set of solutions of the two-dimensional Dirac equation consisting of eigenfunctions of the generator of Lorentz rotations (boost operator). We show that at the surface of the light cone, the boost modes for a fermion field contain the Gelfand delta function of a complex argument. Because of the presence of such a singularity, excluding even a single mode with an arbitrary value of the boost quantum number makes the set of boost modes incomplete. This results in the nonapplicability of the Unruh quantization scheme to a massive fermion field in the two-dimensional Minkowski space-time. Hence, in full accordance with the boson case, the Unruh procedure for a fermion field cannot be used to prove the existence of the Unruh effect. [ABSTRACT FROM AUTHOR]

Whereas boson coherent states with complex parametrization provide an elegant, and intuitive representation, there is no counterpart for fermions using complex parametrization. However, a complex parametrization provides a valuable way to describe amplitude and phase of a coherent beam. Thus we pose the question of whether a fermionic beam can be described, even approximately, by a complex-parametrized coherent state and define, in a natural way, approximate complex-parametrized fermion coherent states. Then we identify four appealing properties of boson coherent states (eigenstate of annihilation operator, displaced vacuum state, preservation of product states under linear coupling, and factorization of correlators) and show that these approximate complex fermion coherent states fail all four criteria. The inapplicability of complex parametrization supports the use of Grassman algebras as an appropriate alternative. [ABSTRACT FROM AUTHOR]

We study the scattering theory of fermion systems subject to a smooth local perturbation with a non-vanishing odd part. We introduce a modified free fermion fields which have an appropriate commutation relations with the free Fock fermion fields. We construct the wave operators using the modified field and prove asymptotic completeness. Our work extends former results on Hilbert space asymptotic completeness. [ABSTRACT FROM AUTHOR]