Generalized Dirac Equation Research Articles

Deformed Hamilton-Jacobi Equations and the Tunneling Radiation of the Higher-Dimensional RN-(A)dS Black Hole

In this paper, we derive the deformed Hamilton-Jacobi equations from the generalized Klein-Gordon equation and generalized Dirac equation. Then, we study the tunneling rate, Hawking temperature and entropy of the higher-dimensional Reissner-Nordstrom de Sitter black hole via the deformed Hamilton-Jacobi equation. Our results show that the deformed Hamilton-Jacobi equations for charged scalar particles and charged fermions have the same expressions. Besides, the modified Hawking temperatures and entropy are related to the mass and charge of the black hole, the cosmology constant, the quantum number of emitted particles, and the term of GUP effects β.

Quantum tunneling from a high dimensional Gödel black hole

Considering quantum gravity effect, we investigate the quantum tunneling from high dimensional Kerr-G\"odel black hole using generalized Dirac equation. As a result, revised tunneling probability is obtained, and the corrected Hawking temperature is also presented.

Fermions in the background of mixed vector–scalar–pseudoscalar square potentials

The general Dirac equation in 1+1 dimensions with a potential with a completely general Lorentz structure is studied. Considering mixed vector–scalar–pseudoscalar square potentials, the states of relativistic fermions are investigated. This relativistic problem can be mapped into a effective Schrödinger equation for a square potential with repulsive and attractive delta-functions situated at the borders. An oscillatory transmission coefficient is found and resonant state energies are obtained. In a special case, the same bound energy spectrum for spinless particles is obtained, confirming the predictions of literature. We showed that existence of bound-state solutions is conditioned by the intensity of the pseudoscalar potential, which possess a critical value.

Fermion unification model based on the intrinsic SU(8) symmetry of a generalized Dirac equation

A natural generalization of the original Dirac spinor into a multi-component spinor is achieved, which corresponds to the single lepton and the three quarks of the first family of the standard model of elementary particle physics. Different fermions result from similarity transformations of the Dirac equation, but apparently there can be no more fermions according to the maximal multiplicity revealed in this study. Rotations in the fermion state space are achieved by the unitary generators of the U(1) and the SU(3) groups, corresponding to quantum electrodynamics (QED based on electric charge) and chromodynamics (QCD based on colour charge). In addition to hypercharge the dual degree of freedom of hyperspin emerges, which occurs due to the duplicity implied by the two related (Weyl and Dirac) representations of the Dirac equation. This yields the SU(2) symmetry of the weak interaction, which can be married to U(1) to generate the unified electroweak interaction as in the standard model. Therefore, the symmetry group encompassing all the three groups mentioned above is SU(8), which can accommodate and unify the observed eight basic stable fermions.

Creation of large scale strong magnetic fields in matter with parity violation

We show that the Standard Model electroweak interaction of ultrarelativistic electrons with nucleons (eN interaction) in a neutron star (NS) permeated by a seed large-scale helical magnetic field provides its growth up to ≳1015 G during a time comparable with the ages of young magnetars ∼104 yr. The magnetic field instability originates from the parity violation in the eN interaction entering the generalized Dirac equation for right and left massless electrons in an external uniform magnetic field. We calculate the averaged electric current given by the solution of the modified Dirac equation containing an extra current for left and right electrons (positrons), which turns out to be directed along the magnetic field. Such current includes both a changing chiral imbalance of electrons and the eN potential given by a constant neutron density in NS. Then we derive the system of the kinetic equations for the chiral imbalance and the magnetic helicity which accounts for the eN interaction. By solving this system, we show that a sizable chiral imbalance arising in a neutron protostar due to the Urca-process eL−+p→N+νeL diminishes very rapidly because of a huge chirality flip rate. Thus the eN term prevails the chiral effect providing a huge growth of the magnetic helicity and the helical magnetic field.

Generalized Dirac Equation with Vector Structural Coefficient and Its Generalized Solutions in Biquaternions Algebra

Generalized Dirac Equation with Vector Structural Coefficient and Its Generalized Solutions in Biquaternions Algebra

GUP Corrected Fermion Tunnelling from 2 + 1 Dimensional Black String

In this paper, using the generalized Dirac equation which is modified by GUP, we study the fermion tunneling from 2 + 1 dimensional black string. Our results show that the Hawking temperature is not only depended on the event horizon of black string but also related to the quantum number of emitted fermion (energy and mass). Meanwhile, we find the GUP can slow down the Hawking temperature increase and lead to the remnants. It implies that the GUP can avoid the evaporation of black holes.

Highly relativistic spin-gravity coupling for fermions

Descriptions of highly relativistic fermions in a gravitational field in the classical (nonquantum) and quantum approaches are discussed. The results following from the Mathisson-Papapetrou equations for a fast spinning particle in Schwarzschild's and Kerr's background are considered. Numerical estimates for electron, proton and neutrino in the gravitational field of black holes are presented.The general relativistic Dirac equation is analyzed from the point of view it is using for the adequate description of highly relativistic fermions in a gravitational field, in the linear and nonlinear spin approximation. It is necessary to have some corrected Dirac equation for a highly relativistic fermion with strong spin-gravity coupling.

Magnetic field instability in a neutron star driven by the electroweak electron-nucleon interaction versus the chiral magnetic effect

We show that the Standard Model electroweak interaction of ultrarelativistic electrons with nucleons ($eN$ interaction) in a neutron star (NS) permeated by a seed large-scale helical magnetic field provides its growth up to $\gtrsim 10^{15}\thinspace\text{G}$ during a time comparable with the ages of young magnetars $\sim 10^4\thinspace\text{yr}$. The magnetic field instability originates from the parity violation in the $eN$ interaction entering the generalized Dirac equation for right and left massless electrons in an external uniform magnetic field. We calculate the averaged electric current given by the solution of the modified Dirac equation containing an extra current for right and left electrons (positrons), which turns out to be directed along the magnetic field. Such current includes both a changing chiral imbalance of electrons and the $eN$ potential given by a constant neutron density in NS. Then we derive the system of the kinetic equations for the chiral imbalance and the magnetic helicity which accounts for the $eN$ interaction. By solving this system, we show that a sizable chiral imbalance arising in a neutron protostar due to the Urca-process $e^-_\mathrm{L} + p\to N + \nu_\mathrm{eL}$ diminishes very rapidly because of a huge chirality flip rate. Thus the $eN$ term prevails the chiral effect providing a huge growth of the magnetic helicity and the helical magnetic field.

Nonstandard Dirac equations for nonstandard spinors

Generalized Dirac equation with operator mass term is presented. Its solutions are nonstandard spinors (NSS) which, like eigenspinoren des Ladungskonjugationsoperators (ELKO), are eigenvectors of the charge conjugation and dual-helicity operators. It is demonstrated that in spite of their noncovariant nature the NSS can serve as a carrier space of a representation of Poincaré group. However, the corresponding boost generators are not manifestly covariant and generate nonlocal momentum dependent transformations, which are presented explicitly. These results can present a new look on group-theoretical grounds of ELKO theories.

Considerations concerning the generalization of the Dirac equations to unstable fermions

We discuss the generalization of the Dirac equations and spinors in momentum space to free unstable spin-$1/2$ fermions taking into account the fundamental requirement of Lorentz covariance. We derive the generalized adjoint Dirac equations and spinors, and explain the very simple relation that exists, in our formulation, between the unstable and stable cases. As an application of the generalized spinors, we evaluate the probability density. We also discuss the behavior of the generalized Dirac equations under time reversal.

Topological crystalline insulators and Dirac octets in antiperovskites

We predict a new class of topological crystalline insulators (TCI) in the anti-perovskite material family with the chemical formula A$_3$BX. Here the nontrivial topology arises from band inversion between two $J=3/2$ quartets, which is described by a generalized Dirac equation for a "Dirac octet". Our work suggests that anti-perovskites are a promising new venue for exploring the cooperative interplay between band topology, crystal symmetry and electron correlation.

Relativistic non-Hermitian quantum mechanics

We develop relativistic wave equations in the framework of the new non-Hermitian $\mathcal{P}\mathcal{T}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that, in particular, the mass matrix be Hermitian also allows for models that have no counterpart in conventional quantum mechanics. For example it is well known that a quartet of Weyl spinors coupled by a Hermitian mass matrix reduces to two independent Dirac fermions; here, we show that the same quartet of Weyl spinors, when coupled by a non-Hermitian but $\mathcal{P}\mathcal{T}$-symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is nonzero. The $\mathcal{P}\mathcal{T}$-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a noninteracting theory it violates $\mathcal{P}$ and $\mathcal{T}$ individually. The relativistic wave equations are reformulated as canonical fermionic field theories to facilitate the study of interactions and are shown to maintain many of the canonical structures from Hermitian field theory, but with new and interesting possibilities permitted by the non-Hermiticity parameter ${m}_{2}$.

Generalized Dirac and Klein-Gordon equations for spinor wavefunctions

A novel method is developed to derive the original Dirac equation and demonstrate that it is the only Poincare invariant dynamical equa- tion for 4-component spinor wavefunctions. New Poincare invariant generalized Dirac and Klein-Gordon equations are also derived. In the non-relativistic limit the generalized Dirac equation gives the general- ized Levy-Leblond equation and the generalized Pauli-Schrodinger equa- tion. The main difference between the original and generalized Dirac equations is that the former and latter are obtained with zero and non- zero phase functions, respectively. Otherwise, both equations describe free elementary particles with spin 1/2, which have all other physical properties the same except their masses. The fact that the generalized Dirac equation describes elementary particles with larger masses is used to suggest that non-zero phase functions may account for the existence of three families of elementary particles in the Standard Model. This suggestion significantly differs from those previously made to account for the three families of particle physics.

Generalized Dirac Equation with Induced Energy-Dependent Potential via Simple Similarity Transformation and Asymptotic Iteration Methods

This study shows how precise simple analytical solutions for the generalized Dirac equation with repulsive vector and attractive energy-dependent Lorentz scalar potentials, position-dependent mass potential, and a tensor interaction term can be obtained within the framework of both similarity transformation and the asymptotic iteration methods. These methods yield a significant improvement over existing approaches and provide more plausible and applicable ways in explaining the pseudospin symmetry’s breaking mechanism in nuclei.

Geometrization of the electromagnetic field and dark matter

Fundamental concepts, symmetries and dynamic equations of the theory of dark matter are derived from the simple relation: everything in the concept of space and the concept of space in everything. It is shown that the electromagnetic field is the singlet state of the dark matter field and, hence, the last may be considered as a generalized electromagnetic field (shortly gef) and a simple solution is given to the old problem of connecting the electromagnetic field with geometric properties of the physical manifold itself. It is shown that gauge fixing renders the generalized electromagnetic field effectively massive while the Maxwell electromagnetic field remains massless. To learn more about interactions between matter and dark matter on the microscopic level (and to recognize the fundamental role of internal symmetry in this case), the general covariant Dirac equation is derived and its natural generalization is considered. The experiment is suggested to test the formulated theory.

From Generalized Dirac Equations to a Candidate for Dark Energy

We consider extensions of the Dirac equation with mass terms m1+iγ5m2 and im1+γ5m2. The corresponding Hamiltonians are Hermitian and pseudo-Hermitian (γ5 Hermitian), respectively. The fundamental spinor solutions for all generalized Dirac equations are found in the helicity basis and brought into concise analytic form. We postulate that the time-ordered product of field operators should yield the Feynman propagator (iϵ prescription), and we also postulate that the tardyonic as well as tachyonic Dirac equations should have a smooth massless limit. These postulates lead to sum rules that connect the form of the fundamental field anticommutators with the tensor sums of the fundamental plane-wave eigenspinors and the projectors over positive-energy and negative-energy states. In the massless case, the sum rules are fulfilled by two egregiously simple, distinguished functional forms. The first sum rule remains valid in the case of a tardyonic theory and leads to the canonical massive Dirac field. The second sum rule is valid for a tachyonic mass term and leads to a natural suppression of the right-handed helicity states for tachyonic particles and left-handed helicity states for tachyonic spin-1/2 antiparticles. When applied to neutrinos, the theory contains a free tachyonic mass parameter. Tachyons are known to be repulsed by gravity. We discuss a possible role of a tachyonic neutrino as a contribution to the accelerated expansion of the Universe “dark energy.”

General Spin Dirac Equation (II)

In an earlier reading [1], we did demonstrate that one can write down a general spin Dirac equation by modifying the usual Einstein energy-momentum equation via the insertion of the quantity “s” which is identified with the spin of the particle. That is to say, a Dirac equation that describes a particle of spin where is the normalised Planck constant, σ are the Pauli 2×2 matrices and s=(±1,±2,±3,…，etc.). What is not clear in the reading [1] is how such a modified energy-momentum relation would arise in Nature. At the end of the day, the insertion by the sleight of hand of the quantity “s” into the usual Einstein energy-momentum equation, would then appear to be nothing more than an idea belonging to the domains of speculation. In the present reading—by making use of the curved spacetime Dirac equations proposed in the work [2], we move the exercise of [1] from the realm of speculation to that of plausibility.

TUNNELING FROM REISSNER-NORDSTRÖM-DE SITTER BLACK HOLE WITH A GLOBAL MONOPOLE

This paper is devoted to investigate the Hawking radiation as a tunneling phenomenon from the Reissner-Nordström-de Sitter black hole with a global monopole. We use the semiclassical WKB approximation to the general covariant charged Dirac equation and evaluate tunneling probability as well as Hawking temperature. We also study the back reaction effects of the emitted spin particles and Bekenstein-Hawking entropy corrections of fermions tunneling through horizon.

Charged fermions tunneling from regular black holes

We study Hawking radiation of charged fermions as a tunneling process from charged regular black holes, i.e., the Bardeen and ABGB black holes. For this purpose, we apply the semiclassical WKB approximation to the general covariant Dirac equation for charged particles and evaluate the tunneling probabilities. We recover the Hawking temperature corresponding to these charged regular black holes. Further, we consider the back-reaction effects of the emitted spin particles from black holes and calculate their corresponding quantum corrections to the radiation spectrum. We find that this radiation spectrum is not purely thermal due to the energy and charge conservation but has some corrections. In the absence of charge, e = 0, our results are consistent with those already present in the literature.