Spinor Fields Research Articles

Dirac–Proca–Maxwell equivalence of dyonic matter with quantum corrections for the quaternionic spinor fields

This research explores a novel approach to obtaining the dyonic Dirac–Proca–Maxwell fields within a single framework. Because Dirac fields are quantum fields for massive fermions, we construct quaternionic fields using a Dirac spinor basis to formulate quantum corrections for electric and magnetic field vectors, electromagnetic field equations, wave equations for scalar and vector potentials, continuity equations, and the propagation of electric and magnetic waves for massive dyons. The quaternionic form of the Dirac spinor fields is used to derive the quantum correction of the electromagnetic field energy of dyonic matter. It is demonstrated that the Maxwell equations for the classical electromagnetic field can be obtained from the quaternionic Dirac spinor fields by applying the quantum approximation condition. Therefore, the quaternionic quantum description of dyonic electromagnetic fields exhibits both wave and particle behaviour for the dynamics of matter particles.

Lagrangian formulation for free 6D infinite spin field

We construct a Lagrangian that describes the dynamics of a six-dimensional free infinite (continuous) spin field in 6D Minkowski space. The Lagrangian is formulated in the framework of the BRST approach to higher spin field theory and is based on a system of constraints defining an irreducible representation of the corresponding Poincaré group. The field realization of generators in the 6D Poincaré algebra and the second-, fourth-, and sixth-order Casimir operators are obtained in explicit form using additional spinor coordinates. Specific aspects of such a realization in six dimensions are discussed. We derive the conditions that determine the irreducible representation 6D infinite spin field and reformulate them as operators in the Fock space forming a first-class algebra in terms of commutators. These operators are used to construct the BRST charge and the corresponding Lagrangian. We prove that the conditions of the irreducible representation are reproduced as the consequence of the Lagrangian equations of motion, which finally provides the correctness of the results obtained.

Majorana Fermion as a Real Spinor Field

Majorana Fermion as a Real Spinor Field

State-Interaction Approach for Evaluating g-Tensors within EOM-CC and RAS-CI Frameworks: Theory and Benchmarks.

Among various techniques designed for studying open-shell species, electron paramagnetic resonance (EPR) spectroscopy plays an important role. The key quantity measured by EPR is the g-tensor, describing the coupling between an external magnetic field and molecular electronic spin. One theoretical framework for quantum chemistry calculations of g-tensors is based on response theory, which involves substantial developments that are specific to the underlying electronic structure models. A simplified and easier-to-implement approach is based on the state-interaction scheme, in which perturbation is included by considering a small number of states. We describe and benchmark the state-interaction approach using equation-of-motion coupled-cluster and restricted-active-space configuration interaction wave functions. The analysis confirms that this approach can deliver accurate results and highlights caveats of applying it, such as a choice of the reference state, convergence with respect to the number of states used in calculations, etc. The analysis also contributes toward a better understanding of challenges in calculations of higher-order properties using approximate wave functions.

Mermin's inequalities in Quantum Field Theory

A relativistic Quantum Field Theory framework is devised for Mermin's inequalities. By employing smeared Dirac spinor fields, we are able to introduce unitary operators which create, out of the Minkowski vacuum |0〉, GHZ-type states. In this way, we are able to obtain a relation between the expectation value of Mermin's operators in the vacuum and in the GHZ-type states. We show that Mermin's inequalities turn out to be maximally violated when evaluated on these states.

Non-thermal photons and a Fermi-Dirac spectral distribution

Although non-intuitive, an accelerated electron along a particular trajectory can be shown to emit classical electromagnetic radiation in the form of a Fermi-Dirac spectral distribution when observed in a particular angular regime. We investigate the relationship between the distribution, spectrum, and particle count. The result for the moving point charge is classical, as it accelerates along an exactly known trajectory. We map to the semi-classical regime of the moving mirror model with a quantized spin-0 field. The scalars also possess a β Bogoliubov coefficient distribution with Fermi-Dirac form in the respective frequency regime.

Dirac Hydrodynamics in 19 Forms

We consider the relativistic spinor field theory re-formulated in polar variables to allow for the interpretation given in terms of fluid variables. After that, the dynamics of spinor fields are converted as dynamics of a special type of spin fluid. We demonstrate that such conversion into dynamical spin fluid is not unique, but it can be obtained through 19 different rearrangements, by explicitly showing the 19 minimal systems of hydrodynamic equations that are equivalent to the Dirac equations.

Magnetization Process in Bilayer Honeycomb Spin Lattice

The magnetization process of the AA-stacked bilayer honeycomb spin lattice in the out-of-plane applied field is examined in the framework of the Ising model and mean field approximation. Competition between different kinds (antiferromagnetic: AF, or ferromagnetic: FM) of intra-layer and inter-layer spin exchange couplings could lead to the first order magnetization process, characterized by sharp jumps in magnetization curves occurring in critical external fields (spin-flop and spin- flip fields). There is only the spin-flip field at very low temperature and its magnitude depends not only on the intra-layer frustration level but also exchange coupling between spin layers. During the magnetization process, the initial AF bilayer honeycomb spin lattice may undergo ferrimagnetic or week-ferromagnetic states before reaching full ferromagnetic saturation state by the spin-flip field. The results of this work can be applied for an explanation of the spin-flip phenomenon registered in the AF bilayer CrI3.

Vector spin Seebeck effect and spin swapping effect in antiferromagnetic insulators with non-collinear spin structure

Antiferromagnets (AFs) are prospective for next-generation high-density and high-speed spintronic applications due to their negligible stray field and ultrafast spin dynamics, notwithstanding the challenges in detecting and manipulating AF order with no magnetization (M = 0). Among the AFs, non-collinear AFs are of particular interest because of their unique properties arising from the non-collinear spin structure and the small magnetization M. In this work, we describe the recently observed vector spin Seebeck effect in non-collinear LuFeO3, where the magneto-thermovoltage under an in-plane temperature gradient, not previously observed, is consistent with the predicted spin swapping effect. Our results shed light on the importance of the non-collinear spin structure in the emerging spin phenomena in non-collinear AFs and offer a new class of materials for AF spintronics and spin caloritronics.

Nonreciprocal terahertz wavefront manipulation based on a magneto-optical metasurface with an orthogonal meta-atom pair

Active wavefront manipulation and nonreciprocal transmission give key performances in beam steering, unidirectional isolation, and multichannel multiplexing. In this work, we propose a magneto-optical (MO) Pancharatnam–Berry (PB) metasurface, which consists of a pair of orthogonal anisotropic Si and InSb columns. This orthogonal meta-atom pair (OMP) structure leads to destructive interference in the geometric phase so that the wavefront manipulation is in the OFF state without a biased magnetic field (BMF). When the BMF is applied, the nonreciprocal transmission effect for different spin states in InSb breaks the original destructive interference, so the devices provide different geometric phase distribution for different magnetic field directions and spin states, achieving the ON state of the nonreciprocal wavefront manipulation, where cross-polarization circular dichroism is higher than 0.98 and the polarization conversion rate is over 97%. Furthermore, based on this mechanism, a beam deflector and a vortex beam generator are designed by arranging the OMP with different azimuthal angles. Compared with ordinary reciprocal wavefront manipulation, this work shows that this MO PB metasurface with OMP structure has irreplaceable functions in the isolation, selection, and conversion of the two conjugate spin beams, providing a unique path for active THz wavefront manipulation.

Sublattice spin reversal and field induced Fe3+ spin-canting across the magnetic compensation temperature in Y1.5Gd1.5Fe5O12 rare-earth iron garnet

In the present work Fe3+ sublattice spin reversal and Fe3+ spin-canting across the magnetic compensation temperature (T) are demonstrated in polycrystalline Y1.5Gd1.5Fe5O12 (YGdIG) by means of in-field Mössbauer spectroscopy measurements. Corroborating in-field Mössbauer measurements, both Fe3+ & Gd3+ sublattice spin reversal has also been manifested in hard x-ray magnetic circular dichroism (XMCD) measurements. From in-field 57 Fe Mössbauer measurements, estimation and analysis of effective internal hyperfine field (H), relative intensity of absorption lines in a sextet elucidated unambiguously the signatures of Fe3+ spin reversal and field induced spin-canting of Fe3+ sublattices across T. Gd L3-edge XMCD signal is observed to consist of an additional spectral feature, identified as Fe3+ magnetic contribution to XMCD spectra of Gd L3-edge, enabling us the extraction of both the sublattices (Fe3+ & Gd3+) information from a single absorption edge analysis. The evolution of the XMCD amplitudes, which is proportional to magnetic moments, as a function of temperature for both magnetic sublattices extracted at the Gd L3-edge reasonably match with values that are extracted from bulk magnetization data of YGdIG and YIG (Y3Fe5O12) and corresponding Fe K-edge XMCD amplitudes for Fe contribution. These measurements pave new avenues to investigate how the magnetic behavior of such complex system acts across the compensation point.

Greybody factors for higher-dimensional non-commutative geometry inspired black holes

Greybody factors are computed for massless fields of spin 0, 1/2, 1, and 2 emitted from higher-dimensional non-commutative geometry inspired black holes. Short-range potentials are used with path-ordered matrix exponentials to numerically calculate transmission coefficients. The resulting absorption cross sections and emission spectra are computed on the brane and compared with the higher-dimensional Schwarzschild–Tangherlini black hole. A non-commutative black hole at its maximum temperature in seven extra dimensions will radiate a particle flux and power of 0.72–0.81 and 0.75–0.81, respectively, times lower than a Schwarzschild–Tangherlini black hole of the same temperature. A non-commutative black hole at its maximum temperature in seven extra dimensions will radiate a particle flux and power of 0.64–0.72 and 0.60–0.64, respectively, times lower than a Schwarzschild–Tangherlini black hole of the same mass.

Coupled quantum vortex kinematics and Berry curvature in real space

The Berry curvature provides a powerful tool to unify several branches of science through their geometrical aspect: topology, energy bands, spin and vector fields. While quantum defects–phase vortices and skyrmions–have been in the spotlight, as rotational entities in condensates, superfluids and optics, their dynamics in multi-component fields remain little explored. Here we use two-component microcavity polaritons to imprint a dynamical pseudospin texture in the form of a double full Bloch beam, a conformal continuous vortex beyond unitary skyrmions. The Berry curvature plays a key role to link various quantum spaces available to describe such textures. It explains for instance the ultrafast spiraling in real space of two singular vortex cores, providing in particular a simple expression–also involving the complex Rabi frequency–for their intricate velocity. Such Berry connections open new perspectives for understanding and controlling highly-structured quantum objects, including strongly asymmetric cases or even higher multi-component fields.

Spin-0 fields and the NP-constants close to spatial infinity in Minkowski spacetime

Newman–Penrose (NP) constants of massless spin-0 fields propagating in Minkowski spacetime are computed close to spatial and null infinity by means of Friedrich’s i0-cylinder. Assuming a certain regularity condition on the initial data ensuring that the field extends analytically to critical sets, it is shown that the NP constants at future I+ and past null infinity I− are independent of each other. In other words, the classical NP constants at I± stem from different parts of the initial data given on a Cauchy hypersurface. In contrast, it is shown that, using a slight generalization of the classical NP constants, the associated quantities (i0-cylinder NP constants) do not require the regularity condition being satisfied and give rise to conserved quantities at I± that are determined by the same piece of initial data, which, in turn, correspond to the terms controlling the regularity of the field. Additionally, it is shown how the conservation laws associated with the NP constants can be exploited to construct, in flat space, heuristic asymptotic-system expansions, which are sensitive to the logarithmic terms at the critical sets.

Quantum magneto-transport properties of monolayers MoSi2N4, WSi2N4, and MoSi2As4

We study the transport properties of monolayers MoSi2N4, WSi2N4, and MoSi2As4 in a perpendicular magnetic field. The Landau level (LL) band structures including spin and exchange field effects are derived and discussed using a low-energy effective model. We show that the LLs band structures of these materials are similar to those of phosphorene and transition-metal dichalcogenides rather than graphene or silicene. The combination of strong spin–orbit coupling and exchange fields reduces the degradation of the LLs, leading to new plateaus in the Hall conductivity and Hall resistivity and new peaks in the longitudinal conductivity and longitudinal resistivity. The effect of the exchange field, carrier density, and LLs band structure on the conductivities and resistivities have been investigated. At high temperatures, the steps in Hall conductivity and resistivity plateaus disappear and reduce to their corresponding classical forms.

Sources of torsion in Poincarè gauge gravity

We study sources for torsion in Poincarè gauge theory in any dimension, signature, and spin. We find that symmetric kinetic terms for non-Yang–Mills bosonic fields of arbitrary rank drive torsion. Our detailed discussion of spin-3/2 Rarita–Schwinger fields shows that they source all independent parts of the torsion. We develop systematic notation for spin-(2k+1)/2 fields and find the spin tensor for arbitrary k in n ge 2k+1 dimensions. For k>0 there is a novel direct coupling between torsion and spinor fields. We also cast the well-known gauge relation between the canonical and Belinfante–Rosenfield energy tensors in terms of different choices of independent variables.

PHYSICAL EXAMPLES OF NONLINEAR DYNAMICAL SYSTEMS

In this study, some important physical systems, which are examples of dynamic systems that exhibit chaotic behavior, are given. These are field models with spinor fields, which are especially important in particle physics. In this study, Duffing, Thirring and Dirac-Gursey systems will be discussed. The Duffing equation is a famous nonlinear differential equation that exemplifies a dynamical system that exhibits chaotic behavior. Various forms of the Duffing equation are used to describe many nonlinear systems. The Duffing equation serves as a test model for us to understand the dynamics of the nonlinear spinor field models we are working on. Thirring system is a relativistic field theory for the interaction of fermions. It is two-dimensional massless system. Since the Thirring system is the simplest nonlinear spinor system, it has an important place in particle physics as a toy model. The Dirac-Gursey system was proposed in 1956 to realize the dream of Heisenberg and his friends. It is the first nonlinear spinor wave equation with four dimensions and conformal invariance. Due to these properties, it has a wider symmetry than the Dirac equation and the equations proposed by Heisenberg et al. Gursey became the first physicist to test conformal invariance in spinor field theories with this system he proposed in 1956.

Tensor gauge boson dark matter extension of the electroweak sector

The existence of dark matter is explained by a new, massive, neutral, non-symmetric, rank-2 tensor gauge boson (hbox {Z}_{{upmu upnu }}-boson). The hbox {Z}_{{upmu upnu }}-boson can be predicted by the tensor gauge boson extension of the Electro Weak (EW) theory, proposed by Savvidy (Phys Lett B 625:341, 2005). The non-symmetric rank-2 tensor hbox {Z}_{{upmu upnu }} can be decomposed into a symmetric (hbox {Z}_{{(upmu upnu )}}) and anti-symmetric (hbox {Z}_{{[upmu upnu ]}}) part. Based on the non-Lagrangian formulation for the free sector of the hbox {R}_{textrm{2}}-theory proposed recently by Criado et al. (Phys Rev D 102:125031, arXiv:2010.02224, 2020), our massive anti-symmetric tensor field hbox {Z}_{{[upmu upnu ]}} corresponds to the massive symmetric spinor field hbox {Z}_{{upalpha upbeta upgamma updelta }} in the (2,0) irrep. For the massive hbox {Z}_{{upalpha upbeta upgamma updelta }} with the hbox {Z}_{textrm{2}}-symmetric Higgs portal couplings to a Standard Model (SM) particle, we compute the self-annihilation cross-section of the hbox {Z}_{{upalpha upbeta upgamma updelta }} dark matter and calculate its relic abundance. We also study the SM-SM particle scattering due to the exchange of the massive-hbox {Z}_{{(upmu upnu )}} symmetric field at a high energy scale. This proposition may have far reaching applications in astrophysics and cosmology.

Spin‐Decoupling and In‐Situ Nuclear Magnetometer with Hyperpolarized Nuclear Spin

AbstractThis paper investigates the dynamical properties of the spin‐coupling ensemble, with a focus on the spin‐decoupling phenomenon. The nuclear spin in such systems is significantly impacted by the electron spin when the main magnetic field approaches the Fermi contact field of nuclear spin, leading to measurement inaccuracies. A comprehensive dynamics model of the electron‐nuclear spin coupling ensemble has been established and analyzed. It proposes that the primary magnetic field augmenting effectively disentangles the precession frequency of the two spin‐coupling species, thereby yielding a spin‐decoupled state. Such a state allows nuclear spin serves as a high sensitive element for magnetic field measurements, while electron spin serves as a probe to acquire the precession of nuclear spin. With proposed method, a magnetic field resolution of 0.75 nT in a 12000 nT environment is achieved, indicating potential for magnetic field detection in geomagnetic environments. It further demonstrates measurements of electron spin Fermi contact interaction and polarization based on spin‐decoupling and in situ nuclear spin precession, results indicate measurement errors close to 1%. These results demonstrate the effectiveness of our approach in improving the accuracy and sensitivity of magnetic field measurements in spin‐coupled systems such as co‐magnetometers, nuclear magnetic resonance gyroscopes, and nuclear magnetometers.

Essential Fierz identities for a fermionic field

For a single fermionic field, an interpretation of the Fierz identities (which establish relations between the bilinear field observables) is given. They appear closely related to the algebraic class (regular or singular) of the spin 2-form S associated to the spinor field. If S ≠ 0, the Fierz identities follow from the 3 + 1 decomposition of the eigenvector equations for S with respect to an inertial laboratory, which makes this interpretation suitable for fermionic particle physics models. When S = 0, the Fierz identities reduce to three constraints on the current densities associated with the spinor field, saying that they are orthogonal, equimodular, the vector current being time-like and the axial one being space-like.