Field Tensor Research Articles

Classical local U(1) gauge invariance in Weyl 2-spinor lenguage and charge quantization from irreducible representations of the gauge group

A new classical 2-spinor approach to U(1) gauge theory is presented in which the usual four-potential vector field is replaced by a symmetric second rank spinor. Following a lagrangian formulation, it is shown that the four-rank spinor representing the Maxwell field tensor has a U(1) local gauge invariance in terms of the electric and magnetic field strengths. When applied to the magnetic field of a monopole, this formulation, via the irreducible representation condition for the gauge group, leads to a quantization condition differing by a factor 2 of the one predicted by Dirac without relying on any kind of singular vector potentials. Finally, the U(1) invariant spinor equations, are applied to electron magnetic resonance which has many applications in the study of materials.

Технология написания проектного кейса в жанре «кейкис»

Is there a necessary and sufficient set of qualitative and quantitative tools (phase and fractal), arranged in a specific sequence, and allowing yourself under time pressure and relatively fast to construct the project chosen for the case study for the problem situation? This research question in the article is given a positive answer. Ten years´ experience of writing individual and group research and educational research cases in the genre KEYKIS within teaching Graduate School of Corporate Management Russian Presidential Academy of National Economy and Public Administration, National Research University "Higher School of Economics" (HSE) and Business University MIRBIS several marketing and managerial disciplines, as well as an extensive consulting practice, allow us to make some generalizations. Show one possible set of qualitative and quantitative tools to build and visualize conceptual models and theories for private research specific cases. The presence of invariant characterization and measurement tools applicable for use on the adjacent flat hierarchies, and networks is showh. It has been shown that it is possible accurate and relatively quick to describe the complex poorly formalized interdisciplinary problematic situation with access to the field (tensor) of alternative solutions regarding adequate external challenges. Examples of practical application of presented equipment.

Chaotic behavior of the lattice Yang-Mills on CUDA

Abstract The Yang-Mills fields plays important role in the strong interaction, which describes the quark gluon plasma. The non-Abelian gauge theory provides the theoretical background understanding of this topic. The real time evolution of the classical fields is derived by the Hamiltonian for SU(2) gauge field tensor. The microcanonical equations of motion is solved on 3 dimensional lattice and chaotic dynamics was searched by the monodromy matrix. The entropy-energy relation was presented by Kolmogorov-Sinai entropy. We used block Hessenberg reduction to compute the eigenvalues of the current matrix. While the purely CPU based algorithm can handle effectively only a small amount of values, the GPUs provide enough performance to give more computing power to solve the problem.

Aspects of neutrino oscillation in alternative gravity theories

Neutrino spin and flavour oscillation in curved spacetime have been studied for the most general static spherically symmetric configuration. Having exploited the spherical symmetry we have confined ourselves to the equatorial plane in order to determine the spin and flavour oscillation frequency in this general set-up. Using the symmetry properties we have derived spin oscillation frequency for neutrino moving along a geodesic or in a circular orbit. Starting from the expression of neutrino spin oscillation frequency we have shown that even in this general context, in high energy limit the spin oscillation frequency for neutrino moving along circular orbit vanishes. We have verified previous results along this line by transforming to Schwarzschild coordinates under appropriate limit. This finally lends itself to the probability of neutrino helicity flip which turns out to be non-zero. While for neutrino flavour oscillation we have derived general results for oscillation phase, which subsequently have been applied to three different gravity theories. One, of them appears as low-energy approximation to string theory, where we have an additional field, namely, dilaton field coupled to Maxwell field tensor. This yields a realization of Reissner-Nordström solution in string theory at low-energy. Next one corresponds to generalization of Schwarzschild solution by introduction of quadratic curvature terms of all possible form to the Einstein-Hilbert action. Finally, we have also discussed regular black hole solutions. In all these cases the flavour oscillation probabilities can be determined for solar neutrinos and thus can be used to put bounds on the parameters of these gravity theories. While for spin oscillation probability, we have considered two cases, Gauss-Bonnet term added to the Einstein-Hilbert action and the f(R) gravity theory. In both these cases we could impose bounds on the parameters which are consistent with previous considerations. In a nutshell, in this work we have presented both spin and flavour oscillation frequency of neutrino in most general static spherically symmetric spacetime, encompassing a vast class of solutions, which when applied to three such instances in alternative theories for flavour oscillation and two alternative theories for spin oscillation put bounds on the parameters of these theories. Implications are also discussed.

Multichannel ULF-MRI Study in Magnetic Unshielded Urban Laboratory Environment

Ultralow field (ULF) magnetic resonance imaging (MRI), which obtains images in the static magnetic field typically on the orders of tens to hundreds of microteslas, exhibits some potential advantages. However, the ULF-MRI system faces the challenge of poor signal-to-noise ratio (SNR). In addition to the introduction of a prepolarization technique and the usage of extremely sensitive superconducting quantum interference devices (SQUIDs), the multisensor parallel imaging technique can also improve the SNR and allow accelerated image acquisition. In this paper, a four-channel ULF-MRI system was built with low-T c SQUID-based second-order axial gradiometer in an urban laboratory environment without magnetic shield. To suppress the temporal field fluctuation and to balance the environment gradient field tensor, an active compensation and a gradient field shimming system were developed. Using the Fourier imaging method and weighted image superposition, the 2-D and 3-D four-channel MRI images of pepper pieces were obtained at a measurement field of 129 μT, i.e., a Larmor frequency of 5.5 kHz with an in-plane resolution of about 2 mm × 2 mm. These results demonstrated the feasibility of performing 2-D and 3-D multisensor parallel ULF MRI in the unshielded urban environment.

Structure of Aristotelian electrodynamics

Aristotelian electrodynamics (AE) describes the regime of a plasma with a very strong electric field that is not shorted out, with the charge current determined completely by pair production and the balance of the Lorentz 4-force against the curvature radiation reaction. Here it is shown how the principal null directions and associated eigenvalues of the field tensor govern AE, and how force-free electrodynamics arises smoothly from AE when the eigenvalues (and therefore the electric field in some frame) vanish. A criterion for validity of AE and force-free electrodynamics is proposed in terms of a pair of ``field curvature scalars'' formed from the first derivative of the principal null directions.

EINSTEIN'S CONNECTION IN 3-DIMENSIONAL ES-MANIFOLD

The manifold $ {}^*{g} - ESX_n $ is a generalized $ n $-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $ {}^*{g}^{ \lambda \nu } $ through the $ ES $-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in $3$-dimensional ${}^*{g}-ESX_3$ and to display a surveyable tnesorial representation of $3$-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the first class.

On the energy-momentum tensor in Moyal space

We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the latter two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice-versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line.

Area terms in entanglement entropy

We discuss area terms in entanglement entropy and show that a recent formula by Rosenhaus and Smolkin is equivalent to the term involving a correlator of traces of the stress tensor in Adler-Zee formula for the renormalization of the Newton constant. We elaborate on how to fix the ambiguities in these formulas: Improving terms for the stress tensor of free fields, boundary terms in the modular Hamiltonian, and contact terms in the Euclidean correlation functions. We make computations for free fields and show how to apply these calculations to understand some results for interacting theories which have been studied in the literature. We also discuss an application to the F-theorem.

Photon momentum transfer in inhomogeneous dielectric mixtures and induced tractor beams

The determination of optical force as a consequence of momentum transfer is inevitably subject to the use of the proper momentum density and stress tensor. It is imperative and valuable to consider the intrinsic scheme of photon momentum transfer, particularly when a particle is embedded in a complex dielectric environment. Typically, we consider a particle submerged in an inhomogeneous background composed of different dielectric materials, excluding coherent illumination or hydrodynamic effects. A ray-tracing method is adopted to capture the direct process of momentum transfer from the complex background medium, and this approach is validated using the modified Einstein–Laub method, which uses only the interior fields of the particle in the calculation. In this way, debates regarding the calculation of the force with different stress tensors using exterior fields can be avoided. Our suggested interpretation supports only the Minkowski approach for the optical momentum transfer to the embedded scatterer while rejecting Peierls's and Abraham's approaches, though the momentum of a stably moving photon in a continuous background medium should be considered to be of the Abraham type. Our interpretation also provides a novel method of realizing a tractor beam for the exertion of negative force that offers an alternative to the use of negative-index materials, optical gain, or highly non-paraxial or multiple-light interference. Support for the Minkowski formulation has been obtained by considering photon momentum transfer for a scatterer at a liquid–gas interface. To shed light on the century-old debate regarding the momentum of light in dielectric media (the so-called Abraham–Minkowski controversy), a team of scientists from Singapore, China and the USA investigated direct momentum transfer from the two media. To do this, they performed ray-tracing calculations combined with modified Einstein–Laub equations that consider only the fields inside the particle, thereby side-stepping problems arising from the use of different stress tensors for fields outside the particle. Their analysis also suggests an alternative way to realize tractor beams (that is, beams that pull rather than push a particle) other than using negative-index materials, optical gain, highly non-paraxial beams or multiple-light interference.

Magnetofluid dynamics in curved spacetime

A grand unified field $\mathcal{M}^{\mu\nu}$ is constructed from Maxwell's Field tensor and appropriately modified flow field, both non-minimally coupled to gravity, to analyze the dynamics of hot charged fluids in curved background space-time. With a suitable $3+1$ decomposition, this new formalism of the hot fluid is then applied to investigate the vortical dynamics of the system. Finally, the equilibrium state for plasma with non-linear coupling through Ricci scalar $R$ to gravity is investigated to derive a double Beltrami equation in curved space-time.

A solvable model for fermion masses on a warped 6D world with the extra 2D sphere

In a warped 6D world with an extra two-dimensional sphere, we propose an exactly solvable model for fermion masses with zero mode. The warp factor is given by ϕ(θ, φ) = sin θ cos φ, which is a solution to the 6D Einstein equation with the bulk cosmological constant Λ and the energy–momentum tensor of the bulk matter fields. Our model provides another possibility of obtaining fermion zero mode, rather than traditional model based on Dirac's monopole.

Three-dimensional tensor controlled-source electromagnetic modeling based on the vector finite-element method

Scalar CSAMT is only suitable for measurements in one and two dimensions perpendicular to geological structures. For complex 3D geoelectric structure, tensor CSAMT is more suitable. In this paper, we discuss 3D tensor CSAMT forward modeling using the vector finite-element method. To verify the feasibility of the algorithm, we calculate the electric field, magnetic field, and tensor impedance of the 3D CSAMT far-zone field in layered media and compare them with theoretical solutions. In addition, a three-dimensional anomaly in half-space is also simulated, and the response characteristics of the impedance tensor and the apparent resistivity and impedance phase are analyzed. The results suggest that the vector finite-element method produces high-precision electromagnetic field and impedance tensor data, satisfies the electric field discontinuity, and does not require divergence correction using the vector finite-element method.

Homogenization models for predicting local field statistics in ellipsoidal particles reinforced composites: Comparisons and validations

This paper validates the performance of analytical homogenization models at predicting the local field statistics in randomly distributed and oriented ellipsoidal particles reinforced composites. The numerical validation was based on a newly introduced load independent metric, which allowed to formulate general conclusions. A large validation campaign was conducted and the Representative Volume Element (RVE) was rigorously determined for each combination of phases mechanical properties, particles volume fraction and aspect ratio. The load independent properties computed numerically were compared to those predicted by a range of analytical models. The study revealed that the original Benveniste’s interpretation of the Mori–Tanaka scheme led to the most accurate first order moments and intra-matrix second order moments, provided that the mechanical properties contrast between the particles and the matrix are low. For higher contrasts, Lielens’ model delivers the most accurate estimates. The self-consistent scheme is the most suited model to predict the intra-particle second order moments when the particles aspect ratio is low. For particles with high aspect ratio, Lielens’ model could be an alternative to the self-consistent scheme. Furthermore, an interpolation model has been developed and it has been shown to predict accurately the mean and covariance tensors of the intraphase stress fields.

Resolving stress tensor components in space from polarized Raman spectra: polycrystalline alumina.

A method of Raman spectroscopic analysis has been proposed for evaluating tensorial stress fields stored in alumina polycrystals with a corundum structure (α-Al2O3). Raman selection rules for all the vibrational modes of the structure were expanded into explicit functions of both 3 Euler angles in space and 4 Raman tensor elements (RTE) of corundum. A theoretical treatment was then worked out according to the phonon deformation potential (PDP) formalism, which explicitly expressed the changes in force constants under stress in matricial form. Close-form solutions could be obtained for the matrix eigenvalues as a function of 9 unknown variables, namely 6 independent stress tensor components and 3 Euler angles in space, the latter parameters being representatives of local crystal orientation. Successively, two separate sets of Raman calibration experiments were performed for the determination of both RTE and PDP constants of the corundum structure of alumina. Calibration experiments provided a quantitative frame to the newly developed Raman formalism. Polarized Raman spectra were systematically recorded in both single-crystalline and polycrystalline samples, with both A1g and Eg vibrational bands being characterized. Regarding polycrystalline samples, a validation of the proposed Raman method could be done through a comparison between Raman and fluorescence data collected at the same locations across an alumina/metal interface embedded in a steeply graded residual stress field.

The Third Polarization of Light

We are all taught that there are only two polarizations of light because Maxwell’s equations only support two polarizations. This is mathematically true for the electromagnetic fields, but we have learned since the days of Maxwell that the “real” electromagnetic field is not the electromagnetic field tensor Fμv (composed of Electric and Magnetic field terms) but rather the electromagnetic vector potential Aμ. When considered carefully, this requires a third polarization of light with very unusual properties. This third polarization of light does not generate electric or magnetic fields but should be detectable by its impact on supercurrents or quantum interference. It is also unavoidable since it automatically appears under Lorentz transformations to different moving frames.

Determination of the First Stress Tensor Invariant of a Complex Steel Sheet Structure from Thermoelastic Stress Analysis

The determination of welded steel sheet assemblies high cycle fatigue properties is a prior concern of the automotive industry. Such assemblies are designed as high-safety parts, for which any fatigue failure is supposed to be prevented. Thus, the determination of complex structures stress field is necessary to design them. Even though finite element models are more and more accurate, experimental methods for the stress field tensors measurement under cyclic loadings are useful to validate those models. The purpose of this work is the experimental determination of the first stress tensor invariant amplitude at the surface of a complex structure under cyclic loading, a car wishbone, with a method based on thermal measurements, the Thermoelastic Stress Analysis (TSA). Parameters which have an influence on the measured temperature at the surface of the structure are studied, including the non-adiabatic behaviour of specimens due to a heterogeneous stress field and the influence of the paint used to measure the temperature with an infra-red camera. All these parameters are taken into account to determine successfully the wishbone stress tensor amplitude during a cyclic test.

Dynamical evolution of a vector field perturbation coupled to the Einstein tensor

We have investigated the wave dynamics of a vector field perturbation coupling to Einstein tensor in the four-dimensional Reissner-Nordstr\"{o}m black hole spacetime. Our results show that besides the dependence on the coupling between the vector field and Einstein tensor, the wave dynamic equation of the vector field perturbation strongly depends on the parity of the perturbation itself, which is quite different from that of the usual vector field perturbation without the coupling in the four-dimensional spacetime. Moreover, we also find that the vector field perturbation with odd parity grows with exponential rate if the coupling strength is stronger than certain a critical value. However, the vector field perturbation with even parity always decays in the Reissner-Nordstr\"{o}m black hole spacetime.

Filtering of matter symmetry properties by circularly polarized nonlinear optics

We propose a direct readout of symmetry information in matter using nonlinear optics. From combinations of circularly and longitudinally polarized optical fields, we construct irreducible spherical field tensors for second- and third-order nonlinear processes. The coupling of these field tensors to the matter susceptibility tensors allows filtering out of the susceptibility symmetries independently of the sample orientation in the laboratory frame. Experimental demonstrations are conducted on microcrystals, in a microscopy configuration compatible with symmetry order imaging.

A higher-spin Chern-Simons theory of anyons

We propose Chern-Simons models of fractional-spin fields interacting with ordinary tensorial higher-spin fields and internal color gauge fields. For integer and half-integer values of the fractional spins, the model reduces to finite sets of fields modulo infinite-dimensional ideals. We present the model on-shell using Fock-space representations of the underlying deformed-oscillator algebra.