Generalized Dirac Equation Research Articles

Rotational influence on fermions within negative curvature wormholes

In this research, we examine relativistic fermions within the rotating frame of negative curvature wormholes. Initially, as is typical in our context, we introduce the wormholes by embedding a curved surface into a higher-dimensional flat Minkowski spacetime. Subsequently, we derive the spacetime metric that characterizes the rotating frame of these wormholes. We then investigate analytical solutions of the generalized Dirac equation within this framework. Through exploring a second-order non-perturbative wave equation, we seek exact solutions for fermions within the rotating frame of hyperbolic and elliptic wormholes, also known as negative curvature wormholes. Our analysis provides closed-form energy expressions, and we generalize our findings to Weyl fermions. By considering the impact of the rotating frame and curvature radius of wormholes, we discuss how these factors affect the evolution of fermionic fields, offering valuable insights into their behavior.

On the Dirac-like equation in 7-component space-time and generalized Clifford-Dirac algebra

The generalized Dirac equation related to 7-component space-time with one time coordinate and six space coordinates has been introduced. Three 8-component Dirac equations have been derived from the same 256-dimensional Clifford-Dirac matrix algebra. Corresponding Clifford-Dirac algebra is considered in the Pauli-Dirac representation of $8 \times 8$ gamma matrices. It is proved that this matrix algebra over the field of real numbers has 256-dimensional basis and it is isomorphic to geometric $\textit{C}\ell^{\texttt{R}}$(1,7) algebra. The corresponding gamma matrix representation of 45-dimensional $\mathrm{SO}(1,9)$ algebra is derived and the way of its generalization to the $\mathrm{SO}(m,n)$ algebra is demonstrated. The Klein-Gordon equation in 7-component space-time is considered as well. The way of corresponding consideration of the Maxwell equations and of equations for an arbitrary spin is indicated.

On Clifford multivector-valued actions, generalized Dirac equation and quantization of branes

We explore the construction of a generalized Dirac equation via the introduction of the notion of Clifford multivector-valued actions, which was inspired by the work of Kanatchikov [Kanatchikov IV. De Donder-Weyl theory and a hypercomplex extension of quantum mechanics to field theory. Rept Math Phys. 1999;43:157–170; Kanatchikov IV. De Donder-Weyl Hamiltonian formulation and precanonical quantization of Vielbein gravity. J Phys Conf Ser. 2013;442:012041] on the De Donder-Weyl formulation of field theory. Crucial in this construction is the evaluation of the exponentials of multivectors associated with Clifford (hypercomplex) analysis. Exact matrix solutions (instead of spinors) of the generalized Dirac equation in D = 2 , 3 space–time dimensions are found. This formalism can be extended to curved space–time backgrounds. We conclude by proposing a wave-functional equation governing the quantum dynamics of branes living in C-spaces (Clifford spaces), and which is based on the De Donder–Weyl Hamiltonian formulation of field theory.

Gravidynamics, spinodynamics and electrodynamics within the framework of gravitational quantum field theory

By noticing the fact that the charged leptons and quarks in the standard model are chirality-based Dirac spinors since their weak interaction violates maximally parity symmetry though they behave as Dirac fermions in electromagnetic interaction, we show that such a chirality-based Dirac spinor possesses not only electric charge gauge symmetry U(1) but also inhomogeneous spin gauge symmetry WS(1,3) = SP(1,3)$\rtimes$W$^{1,3}$, which reveals the nature of gravity and spacetime. The gravitational force and spin gauge force are governed by the gauge symmetries $W^{1,3}$ and SP(1,3), respectively, and a biframe spacetime with globally flat Minkowski spacetime as base spacetime and locally flat gravigauge spacetime as a fiber is described by the gravigauge field through emergent non-commutative geometry. The gauge-geometry duality and renormalizability in gravitational quantum field theory (GQFT) are carefully discussed. A detailed analysis and systematic investigation on gravidynamics and spinodynamics as well as electrodynamics are carried out within the framework of GQFT. A full discussion on the generalized Dirac equation and Maxwell equation as well as Einstein equation and spin gauge equation is made in biframe spacetime. New effects of gravidynamics as extension of general relativity are particularly analyzed. All dynamic equations of basic fields are demonstrated to preserve the spin gauge covariance and general coordinate covariance due to the spin gauge symmetry and emergent general linear group symmetry GL(1,3,R), so they hold naturally in any spinning reference frame and motional reference frame.

Near-Horizon Thermodynamics of Hairy Black Holes from Gravitational Decoupling

The horizon structure and thermodynamics of hairy spherically symmetric black holes generated by the gravitational decoupling method are carefully investigated. The temperature and heat capacity of the black hole is determined, as well as how the hairy parameters affect the thermodynamics. This allows for an analysis of thermal stability and the possible existence of a remanent black hole. We also calculate the Hawking radiation corrected by the generalized uncertainty principle. We consider the emission of fermions and apply the tunneling method to the generalized Dirac equation. This shows that, despite the horizon location being the same as the Schwarzschild one for a suitable choice of parameters, the physical phenomena that occur near the horizon of both black holes are qualitatively different.

Relativistic free fermions in spiral dislocation space–time with a distortion of a radial line into a spiral

Relativistic quantum mechanics of free fermions in the presence of the spiral dislocation of space–time with a distortion of a radial line into a spiral is studied within the Katanaev–Volovich geometric approach. The generalized Dirac equation in this background is constructed. Exact closed-form solutions are found by reducing the problem to that of a nonrelativistic two-dimensional [Formula: see text]-problem with a complex coupling constant. The influence of the defect parameter related to the spiral dislocation on these solutions is investigated. We also study the charge density of free fermions in the presence of such a spiral dislocation in space–time. Based on the Bender–Boettcher approach for non-Hermitian Hamiltonians we study, in addition, bound-state solutions of the system.

Generalized Dirac Equation for a particle in a gravitational field

Generalized Dirac Equation for a particle in a gravitational field

Wave-particle duality and the zitterbewegung

In previous work, the Hamilton-Jacobi equation has been associated with the metrics of general relativity and shown to be a generalized Dirac equation for quantum mechanics. This lends itself to a natural definition of wave-particle duality in quantum mechanics. This theory is now further developed to show that a free spinless quantum particle moving with velocity v obeys the standard wave equation of electro-magnetism. We also discuss the implications for the zitterbewegung problem and its relationship to isotropy. Moreover, it is also shown that for the theory to be consistent, the momentum defined by the Hamilton-.!acobi function presupposes the existence of a universal parameter internal to the system. In the case of particles with mass this invariant can be defined by dX = dt/m(t) where t has the units of time and m = m(t) has the units of mass.

Dirac equation from the extended uncertainty principle

The existence of a minimal momentum modifies the Heisenberg’s uncertainty principle, which implies modifications of the Dirac equation. In this work, we study the influence of this minimal uncertainty in the particle’s momentum to deduce a generalized Dirac equation and solve its eigenvalue problem for a free particle and a particle within a gravitational field.

Planar Hall effect with sixfold oscillations in a Dirac antiperovskite

The planar Hall effect (PHE), wherein a rotating magnetic field in the plane of a sample induces oscillating transverse voltage, has recently garnered attention in a wide range of topological metals and insulators. The observed twofold oscillations in ρyx as the magnetic field completes one rotation are the result of chiral, orbital, and/or spin effects. The antiperovskites A3BO (A=Ca, Sr, Ba; B=Sn, Pb) are topological crystalline insulators whose low-energy excitations are described by a generalized Dirac equation for fermions with total angular momentum J=32. We report unusual sixfold oscillations in the PHE of Sr3SnO, which persisted nearly up to room temperature. Multiple harmonics (twofold, fourfold, and sixfold), which exhibited distinct field and temperature dependencies, were detected in ρxx and ρyx. These observations are more diverse than those in other Dirac and Weyl semimetals and point to a richer interplay of microscopic processes underlying the PHE in the antiperovskites.Received 10 November 2020Accepted 4 March 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013268Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasHall effectMagnetotransportTopological materialsCondensed Matter, Materials & Applied Physics

Thermodynamic Phase Transition of the Spherically Black Hole with Global Monopole Under GUP

In this paper, considering the influence of the principle of generalized uncertainty (GUP), the phase transition of a Schwarzschild black hole with global monopole is discussed. First, we use the generalized Dirac equation to obtain corrected Hawking temperature, local temperature, black hole residues, black hole entropy, thermal capacity, and other thermodynamic quantities. Then, we analyze the effects of generalized uncertainty parameters and the monopole parameter on phase transitions. Finally, we study the thermodynamic stability and phase transition structure under the influence of GUP. The results show that, for the black hole with global monopole, there are first–order and second–order phase transitions. In addition, the general uncertainty parameter and monopole parameter will affect the black hole residues.

Entropy Correction of Kerr-de Sitter Black Hole Influenced by GUP

In this paper, the tunneling of fermions and scalar particles from a Kerr-de Sitter (KdS) black hole are investigated using the generalized Dirac equation and the generalized form of Hamilton-Jacobi equation respectively by taking quantum gravity effects into account. The modified Hawking temperatures at the event horizon of KdS black hole for the emission of fermions and scalar particles are obtained. The entropy corrections of KdS black hole including the logarithmic term are also obtained.

GUP effects on Hawking temperature in Riemann space-time

In this paper, the modified Hawking temperature of a static Riemann space-time is studied using the generalized Klein–Gordon equation and the generalized Dirac equation. Applying the Kerner–Mann quantum tunneling method, the modified Hawking temperatures for scalar particles and fermions that cross the event horizon of the black hole have been derived. We observe that the quantum gravity effects reduce the rise of thermal radiation temperature of the black hole.

Towards a Z3-graded approach to quarks’ symmetries

Colour SU(3) group is an exact symmetry of Quantum Chromodynamics, which describes strong interactions between quarks and gluons. Supplemented by two internal symmetries, SU(2) and U(1), it serves as the internal symmetry of the Standard Model, describing as well the electroweak interactions of quarks and leptons. The colour SU(3) symmetry is exact, while two other symmetries are broken by means of the Higgs-Kibble mechanism. The three colours and fractional quarks charges with values 1/3 and 2/3 suggest that the cyclic group Z3 may play a crucial role in quark field dynamics.In this paper we consequently apply the Z3 symmetry to field multiplets describing colour quark fields. Generalized Dirac equation for coloured 12-component spinors is introduced and its properties are discussed. Imposing Z3-graded Lorentz and Poincaré covariance leads to enlargement of quark fields multiplets and incorporates additional Z2 × Z3 symmetry which leads to the appearance of three generations (families) of distinct quark doublets.

Rotation effect on spin current in curved space-time

The spin-orbit interaction and spin Hall effect have drawn special attention. Not only theoretical predictions have been made, but also the generation of spin currents has been achieved in experiment. In this paper, we study the spin current and the spin Hall conductivity under the influence of rotation in the curved space-time. Our work shows that the nontrivial geometries could modify the spin-orbital interaction. By using the extended Drude model, we calculate the spin-dependent force and obtain a correction to this force by non-mediocre geometry. When considering the rotation effect, the general Dirac equation is given. The Hamiltonian under the non-relativistic approximation is obtained by the Foldy-Wouthuysen transform. According to this, we calculate the spin current and spin Hall conductance. The polarization vector is deformed due to the effect of the rotation in the curved space-time. The magnitude and direction of the spin current are changed because of the correction to rotation, and the spin Hall conductivity. The nontrivial space-time geometry leads to the anisotropic nature of the spin current. Our work uses a general method that does not depend on the model, so the result can be used to analyze the electromagnetic dynamics of charged spin particles in quantum Hall systems, and it also helps to theoretically study the defects in crystals. Our results can also be extended to the optical subsystem. Considering the spin effect of photons, based on the spin-orbit coupling of photon, a light splitting phenomenon emerges in an inhomogeneous medium, which is the spin hall effect of photon. Our discussion has a certain reference value for studying the behavior of the photonic spin Hall effect in the static gravitational field. At the same time, using the optical chips to simulate curved space-time, photon manipulation and precision measurement can give some theoretical support.

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime**Supported by National Science Foundation of China (NSFC) (11690022, 11475237, 11121064) and Strategic Priority Research Program of the Chinese Academy of Sciences (XDB23030100) as well as the CAS Center for Excellence in Particle Physics (CCEPP)

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincaré symmetry P(1,5)=SO(1,5)⋉P1,5 as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.

Quantum Gravity Effects on Hawking Radiation of Schwarzschild-de Sitter Black Holes

The correction of Hawking temperature of Schwarzschild-de Sitter (SdS) black hole is investigated using the generalized Klein-Gordon equation and the generalized Dirac equation by taking the quantum gravity effects into account. We derive the corrected Hawking temperatures for scalar particles and fermions crossing the event horizon. The quantum gravity effects prevent the rise of temperature in the SdS black hole. Besides correction of Hawking temperature, the Hawking radiation of SdS black hole is also investigated using massive particles tunneling method. By considering self gravitation effect of the emitted particles and the space time background to be dynamical, it is also shown that the tunneling rate is related to the change of Bekenstein-Hawking entropy and small correction term (1 + 2β m 2). If the energy and the angular momentum are taken to be conserved, the derived emission spectrum deviates from the pure thermal spectrum. This result gives a correction to the Hawking radiation and is also in agreement with the result of Parikh and Wilczek.

Classification of Particles at Arbitrary Quantity of Generations. I. Hadrons

New classification of particles is proposed. This classification is based on U(Nf,g) ×SU(3c)×SU(4, fs)×O(3) -group, where U(Nf,g) corresponds to the particle generations, SU(3,c) - to the color, SU(4,fs) - to the flavor and the spin (instead of known SU(6,fs) -group), and O(3) - to the orbital excitation with the L -momentum. The Nf -number equals the quantity of fermion generations. From the convergence of the integrals corresponding to the Green functions for generalized Dirac equations and the continuity of these functions it follows that the minimal quantity of the Nf -number equals six. The homogeneous solutions of derived equations are sums of fields, corresponding to particles with the same values of the spin, the electric charge, the parities, but with different masses. Such particles are grouped into the kinds (families, dynasties) with members which are the particle generations. For example, the electronic kind (e1 = e, e2 = μ, e3 =τ , e4, e5, e6, ), the kind of up-quarks (U1 = u, U2 = c, U3 = t, U4, U5, U6, ⋅⋅ ), and the kind of down-quarks (D1 = d, D2 = s, D4 = b, D4, D5, D6, ⋅⋅ ) can exist. Massless neutrino can be one only. The photonic and the gluonic kinds must include massive particles in addition to usual the photon and the gluon. At NF = 6 the nucleons and Δ(1232) belong to the 56×1×20×1 - representation. Lagrangians for the generalized Dirac equations of arbitrary order are derived.

Solution of generalized Dirac equation for Eckart plus Hulthen central potential combined with modified Hylleraas like tensor potential using Romanovski polynomial method

Romanovski Polynomial method was used to analyze of Dirac equation with Eckart plus Hulthen central potential combined with modified Hylleraas like tensor potential on spin symmetry case. By using parameter and variable substitution, the Dirac equation was reduced into one dimensional Schrodinger like equation with centrifugal approximation that can be solved using Romanovski polynomial. The relativistic energy spectra is obtained from the relativistic energy equation by using Matlab R2008b software. The relativistic energy with quantum number and spin orbit quantum number variations were obtained. By using matlab R2008b software, visualisasion of the relativistic energy spectra with quantum number variasion were obtained.

Fundamental Fermion Interactions via Vector Bosons of Unified SU(2)⊗SU(4) Gauge Fields

Employing the fermion unification model based on the intrinsic SU(8) symmetry of a generalized Dirac equation, we discuss the fundamental interactions under the SU(8)=SU(2)$\otimes$SU(4) symmetry group. The physics involved can describe all fermions, the leptons (electron and neutrino), and the coloured up and down quarks of the first generation in the standard model (SM) by a complex SU(8) octet of Dirac spinor fields. The fermion interactions are found to be mediated by the unified SU(4) and SU(2) vector gauge boson fields, which include the photon, the gluons, and the bosons $Z$ and $W$ as well known from the SM, but also comprise new ones, namely three coloured $X$ bosons carrying a fractional hypercharge of $\pm4/3$ and transmuting leptons into quarks and vice versa. The full covariant derivative of the model is derived and discussed. The Higgs mechanism gives mass to the $Z$ and $W$ bosons, but also permits one to derive the mass of the coloured $X$ boson, for which depending on the choice of the values of the coupling constant, the estimates are 35~GeV or 156~GeV, values that are well within reach of the LHC. The scalar Higgs field can also lend masses to the fermions and fix their physical values for given appropriate coupling constants to that field.