Unification of massless field equations solutions for any spin

A unification in terms of exact solutions for massless Klein–Gordon, Dirac, Maxwell, Rarita– Schwinger, Einstein, and bosonic and fermionic fields of any spin is presented. The method is based on writing all of the relevant dynamical fields in terms of products and derivatives of pre–potential functions, which satisfy d’Alambert equation. The coupled equations satisfied by the pre–potentials are non-linear. Remarkably, there are particular solutions of (gradient) orthogonal pre–potentials that satisfy the usual wave equation which may be used to construct exact non–trivial solutions to Klein–Gordon, Dirac, Maxwell, Rarita–Schwinger, (linearized and full) Einstein and any spin bosonic and fermionic field equations, thus giving rise to an unification of the solutions of all massless field equations for any spin. Some solutions written in terms of orthogonal pre–potentials are presented. Relations of this method to previously developed ones, as well as to other subjects in physics are pointed out.

Noether symmetry approach in f (T, B) teleparallel gravity with a fermionic field

In this work, we consider a homogeneous and isotropic cosmological model of the universe in f (T, B) gravity with non-minimally coupled fermionic field. In order to find the form of the coupling function F(Ψ), the potential function V (Ψ) of the fermionic field and the function f (T, B), we found through the Noether symmetry approach. The results obtain are coincide with the observational data that describe the late-time accelerated expansion of the universe.

Polynomial inflation and dark matter

We present a minimal UV complete framework to embed inflation and dark matter by extending the standard model with a singlet real scalar field (the inflaton) and a singlet fermionic field acting as dark matter. The inflaton features the most general renormalizable polynomial up to quartic order, which is flat due to the existence of a perturbed inflection-point, comfortably fitting CMB measurements. We also analyze (p)reheating by considering the Higgs production via inflaton decay. In the early universe, dark matter can be generated by the mediation of gravitons or inflatons. However, the production via the direct decay of the inflatons dominates, making viable a large range of dark matter masses, from $${\mathcal {O}}(10^{-5})$$ O ( 10 - 5 ) GeV to $${\mathcal {O}}(10^{11})$$ O ( 10 11 ) GeV.

Quantum unitary dynamics of a charged fermionic field and Schwinger effect

In quantum field theory, particle creation occurs, in general, when an intense external field, such as an electromagnetic field, breaks time translational invariance. This leads to an ambiguity in the definition of the vacuum state. In cosmological backgrounds this ambiguity has been reduced by imposing that the quantization preserves the symmetries of the system and that the dynamics is unitarily implemented. In this work, we apply these requirements to the quantization of a massive charged fermionic field coupled to a classical time-dependent homogeneous electric field, extending previous studies done for a scalar field. We characterize the quantizations fulfilling the criteria above and we show that they form a unique equivalence class of unitarily related quantizations, which provide a well-defined number of created particles at all finite times.

Quantum Bohmian description of a primordial universe with Fermionic and Bosonic sources

We present a model of an early universe where the sources of gravitational effects are a scalar field, a relativistic fluid based on Schutz’s model and a self-interacting fermionic field. From the classical analysis based on the Hamiltonian formalism we show that the scale factor of the universe can be expressed in terms of a conformal time that emerges from the fluid’s degrees of freedom. From the Wheeler–DeWitt equation, a wave packet solution as function of the conformal time is determined. It is shown that the combination of the scalar and the fermionic field furnishes a consistent quantum regime and a smooth transition to the classical description, working with the aid of the Bohmian mechanics and in particular with the concept of quantum potential. The influence of the presence of the scalar field is also discussed.

Casimir Effect for Fermion Condensate in Conical Rings

The fermion condensate (FC) is investigated for a (2+1)-dimensional massive fermionic field confined on a truncated cone with an arbitrary planar angle deficit and threaded by a magnetic flux. Different combinations of the boundary conditions are imposed on the edges of the cone. They include the bag boundary condition as a special case. By using the generalized Abel-Plana-type summation formula for the series over the eigenvalues of the radial quantum number, the edge-induced contributions in the FC are explicitly extracted. The FC is an even periodic function of the magnetic flux with the period equal to the flux quantum. Depending on the boundary conditions, the condensate can be either positive or negative. For a massless field the FC in the boundary-free conical geometry vanishes and the nonzero contributions are purely edge-induced effects. This provides a mechanism for time-reversal symmetry breaking in the absence of magnetic fields. Combining the results for the fields corresponding to two inequivalent irreducible representations of the Clifford algebra, the FC is investigated in the parity and time-reversal symmetric fermionic models and applications are discussed for graphitic cones.

Fermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermions

We construct a mass dimension one fermionic field associated with flag-dipole spinors. These spinors are related to Elko (flag-pole spinors) by a one-parameter matrix transformation $${\mathcal {Z}}(z)$$ Z ( z ) where z is a complex number. The theory is non-local and non-covariant. While it is possible to obtain a Lorentz-invariant theory via $$\tau $$ τ -deformation, we choose to study the effects of non-locality and non-covariance. Our motivation for doing so is explained. We show that a fermionic field with $$|z|\ne 1$$ | z | ≠ 1 and $$|z|=1$$ | z | = 1 are physically equivalent. But for fermionic fields with more than one value of z, their interactions are z-dependent thus introducing an additional fermionic degeneracy that is absent in the Lorentz-invariant theory. We study the fermionic self-interaction and the local U(1) interaction. In the process, we obtained non-local contributions for fermionic self-interaction that have previously been neglected. For the local U(1) theory, the interactions contain time derivatives that renders the interacting density non-commutative at space-like separation. We show that this problem can be resolved by working in the temporal gauge. This issue is also discussed in the context of gravity.

A Gauge Theory that Mixes Bosonic and Fermionic Gauge Fields

Using a gauge symmetry derived by applying the Dirac constraint formalism to supergravity with a cosmological term in 2 + 1 dimensions, we construct a gauge theory with many characteristics of Yang-Mills theory. The gauge transformation mixes two Bosonic fields and one Fermionic field.

Vacuum bosonic currents induced by a compactified cosmic string in dS background

In this paper, we study the vacuum bosonic currents in the geometry of a compactified cosmic string in the background of the de Sitter spacetime. The currents are induced by magnetic fluxes, one running along the cosmic string and another one enclosed by the compact dimension. To develop the analysis, we obtain the complete set of normalized bosonic wave functions obeying a quasiperiodicity condition. In this context, we calculate the azimuthal and axial current densities and we show that these quantities are explicitly decomposed into two contributions: one originating from the geometry of a straight uncompactified cosmic string and the other induced by the compactification. We also compare the results with the literature in the case of a massive fermionic field in the same geometry.

Liouville theory and matrix models: a Wheeler DeWitt perspective

We analyse the connections between the Wheeler DeWitt approach for two dimensional quantum gravity and holography, focusing mainly in the case of Liouville theory coupled to c = 1 matter. Our motivation is to understand whether some form of averaging is essential for the boundary theory, if we wish to describe the bulk quantum gravity path integral of this two dimensional example. The analysis hence, is in a spirit similar to the recent studies of Jackiw-Teitelboim (JT)-gravity. Macroscopic loop operators define the asymptotic region on which the holographic boundary dual resides. Matrix quantum mechanics (MQM) and the associated double scaled fermionic field theory on the contrary, is providing an explicit “unitary in superspace” description of the complete dynamics of such two dimensional universes with matter, including the effects of topology change. If we try to associate a Hilbert space to a single boundary dual, it seems that it cannot contain all the information present in the non-perturbative bulk quantum gravity path integral and MQM.