Dirac Current Research Articles

Lightlike conformal reduction of 6d (1, 0) theories

We study 6d (1, 0) superconformal theories. These have a natural lightlike conformal Killing vector, the Dirac current. We perform a conformal dimensional reduction along the Dirac current down to five-dimensions in such a way that we always preserve at least two real supercharges.

DIRAC current, upcoming and planned capabilities and technologies

DIRAC is the interware for building and operating large scale distributed computing systems. It is adopted by multiple collaborations from various scientific domains for implementing their computing models. DIRAC provides a framework and a rich set of ready-to-use services for Workload, Data and Production Management tasks of small, medium and large scientific communities having different computing requirements. The base functionality can be easily extended by custom components supporting community specific workflows. DIRAC is at the same time an aging project, and a new DiracX project is taking shape for replacing DIRAC in the long term. This contribution will highlight DIRAC’s current, upcoming and planned capabilities and technologies, and how the transition to DiracX will take place. Examples include, but are not limited to, adoption of security tokens and interactions with Identity Provider services, integration of Clouds and High Performance Computers, interface with Rucio, improved monitoring and deployment procedures.

Some recent results for SU(3) and octonions within the geometric algebra approach to the fundamental forces of nature

Different ways of representing the group within a Geometric Algebra approach are explored. As part of this, we consider characteristic multivectors for and how these are linked with decomposition of generators into commuting bivectors. The setting for this work is within a 6d Euclidean Clifford Algebra. We then go on to consider whether the fundamental forces of particle physics might arise from symmetry considerations in just the 4d geometric algebra of spacetime—the STA. As part of this, a representation of is found wholly within the STA, involving preservation of a bivector norm. We also show how Octonions can be fully represented within the Spacetime Algebra, which we believe will be useful in making them understandable and accessible to a new community in Physics and Engineering. The two strands of the paper are drawn together in showing how preserving the octonion norm is the same as preserving the timelike part of the Dirac current of a particle. This suggests a new model for the symmetries preserved in particle physics. Following on from work by Günaydin and Gürsey on the link between quarks, and octonions, and by Furey on chains of octonionic multiplications, we show how both of these fit well within our scheme and give some wholly STA versions of the operations involved, which in the cases considered have easily understandable equivalents in terms of 4d geometry. Links with larger groups containing , such as and , are also considered.

Transmission through potential barriers with a generalised Fermi–Dirac current

We study the effect of the shape of different potential barriers on a transmitted charged current whose fermionic population is not monoenergetic but is described by means of an energy spectrum. The generalised kappa Fermi–Dirac distribution function is able to take into account both equilibrium and non-equilibrium populations of particles by changing the kappa index. Moreover, the corresponding current density can be evaluated using such a distribution. Subsequently, this progressive charged density arrives at the potential barrier, which is considered under several shapes, and the corresponding transmission factor is evaluated. This permits a comparison of the effects for different barriers as well as for different energy states of the incoming current.

Gamma-ray radiation effects in graphene-based transistors with h-BN nanometer film substrates

Radiation effects on graphene field effect transistors (GFETs) with hexagonal boron nitride (h-BN) thin film substrates are investigated using 60Co gamma-ray radiation. This study examines the radiation response using many samples with varying h-BN film thicknesses (1.6 and 20 nm thickness) and graphene channel lengths (5 and 10 μm). These samples were exposed to a total ionizing dose of approximately 1 Mrad(Si). I-V measurements were taken at fixed time intervals between irradiations and postirradiation. Dirac point voltage and current are extracted from the I-V measurements, as well as mobility, Dirac voltage hysteresis, and the total number of GFETs that remain properly operational. The results show a decrease in Dirac voltage during irradiation, with a rise of this voltage and permanent drop in Dirac current postirradiation. 1.6 nm h-BN substrate GFETs show an increase in mobility during irradiation, which drops back to preirradiation conditions in postirradiation measurements. Hysteretic changes to the Dirac voltage are the strongest during irradiation for the 20 nm thick h-BN substrate GFETs and after irradiation for the 1.6 nm thick h-BN GFETs. Failure rates were similar for most GFET types during irradiation; however, after irradiation, GFETs with 20 nm h-BN substrates experienced substantially more failures compared to 1.6 nm h-BN substrate GFETs.

Consistent gauge interaction involving dynamical coupling and anomalous current

We show a possible way to construct a consistent formalism where the effective electric charge can change with space and time without destroying the gauge invariance. In the previous work[Formula: see text] we took the gauge coupling to be of the form [Formula: see text] where [Formula: see text] is an auxiliary field, [Formula: see text] is a scalar field and the current [Formula: see text] is the Dirac current. This term produces a constraint [Formula: see text] which can be related to MIT bag model by boundary condition. In this paper, we show that when we use the term [Formula: see text], instead of the auxiliary field [Formula: see text], there is a possibility to produce a theory with dynamical coupling constant, which does not produce any constraint or confinement. The coupling [Formula: see text] where [Formula: see text] is an anomalous current is also discussed.

On the disformal invariance of the Dirac equation

We analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field acting on the metric tensor. Using the Weyl–Cartan formalism, we construct a large class of disformal maps between different metric tensors, respecting the order of differentiability of the Dirac operator and satisfying the Clifford algebra in both metrics. We split the analysis in some cases according to the spinor mass and the norm of the Dirac current, exhibiting sufficient conditions to find classes of solutions which keep the Dirac operator invariant under the action of the disformal group.

On the question of current conservation for the two-body Dirac equations of constraint theory

The two-body Dirac (2BD) equations of constraint theory are of special interest not only in view of applications for phenomenological calculations of mesonic spectra but also because they avoid no-go theorems about relativistic interactions. Furthermore, they provide a quantum mechanical description in a manifestly Lorentz invariant way using the concept of a multi-time wave function. In this paper, we place them into the context of the multi-time formalism of Dirac, Tomonaga and Schwinger for the first time. A general physical and mathematical framework is outlined and the mechanism which permits relativistic interaction is identified. The main requirement derived from the general framework is the existence of conserved tensor currents with a positive component which can play the role of a probability density. We analyze this question for a general class of 2BD equations thoroughly and comprehensively. While the free Dirac current is not conserved, it is possible to find replacements. Improving on previous research, we achieve definite conclusions whether restrictions of the function space or of the interaction terms can guarantee the positive definiteness of the currents—and whether such restrictions are physically adequate. The consequences of the results are drawn, with respect to both applied and foundational perspectives.

Charged conformal Killing spinors

We study the twistor equation on pseudo-Riemannian Spinc-manifolds whose solutions we call charged conformal Killing spinors (CCKSs). We derive several integrability conditions for the existence of CCKS and study their relations to spinor bilinears. A construction principle for Lorentzian manifolds admitting CCKS with nontrivial charge starting from CR-geometry is presented. We obtain a partial classification result in the Lorentzian case under the additional assumption that the associated Dirac current is normal conformal and complete the classification of manifolds admitting CCKS in all dimensions and signatures ≤5 which has recently been initiated in the study of supersymmetric field theories on curved space.

Confining boundary conditions from dynamical coupling constants for Abelian and non-Abelian symmetries

The present work represents among other things a generalization to the non-Abelian case of our previous result where the Abelian case was studied. In the U(1) case the coupling to the gauge field contains a term of the form g(ϕ)jμ(Aμ +∂μB), where B is an auxiliary field and jμ is the Dirac current. The scalar field ϕ determines the local value of the coupling of the gauge field to the Dirac particle. The consistency of the equations determines the condition ∂μϕjμ = 0 which implies that the Dirac current cannot have a component in the direction of the gradient of the scalar field. As a consequence, if ϕ has a soliton behavior, we obtain that jμ cannot have a flux through the wall of the bubble, defining a confinement mechanism where the fermions are kept inside those bags. In this paper, we present more models in Abelian case which produce constraint on the Dirac or scalar current and also spin. Furthermore a model that gives the MIT confinement condition for gauge fields is obtained. We generalize this procedure for the non-Abelian case and we find a constraint that can be used to build a bag model. In the non-Abelian case, the confining boundary conditions hold at a specific surface of a domain wall.

Rigid supersymmetry, conformal coupling and twistor spinors

We investigate the relationship between conformal and spin structure on lorentzian manifolds and see how their compatibility influences the formulation of rigid supersymmetric field theories. In dimensions three, four, six and ten, we show that if the Dirac current associated with a generic spinor defines a null conformal Killing vector then the spinor must obey a twistor equation with respect to a certain connection with torsion. Of the theories we consider, those with classical superconformal symmetry in Minkowski space can be reformulated as rigid supersymmetric theories on any lorentzian manifold admitting twistor spinors. In dimensions six and ten, we also describe rigid supersymmetric gauge theories on bosonic minimally supersymmetric supergravity backgrounds.

Confining boundary conditions from dynamical coupling constants

It is shown that it is possible to consistently and gauge invariantly formulate models where the coupling constant is a non-trivial function of a scalar field. In the U(1) case, the coupling to the gauge field contains a term of the form g(ϕ)jμ(Aμ+∂μB) where B is an auxiliary field and jμ is the Dirac current. The scalar field ϕ determines the local value of the coupling of the gauge field to the Dirac particle. The consistency of the equations determines the condition ∂μϕjμ=0 which implies that the Dirac current cannot have a component in the direction of the gradient of the scalar field. As a consequence, if ϕ has a soliton behaviour, like defining a bubble that connects two vacua, we obtain that the Dirac current cannot have a flux through the wall of the bubble, defining a confinement mechanism where the fermions are kept inside those bags. Consistent models with time dependent fine structure constant can be also constructed

Computational Determination of the Dirac-Theory Adjunctator

A number of particle properties stem from the use ofγ0as adjunctator (Bargmann-Pauli) in the Dirac theory (spin alignment, Dirac current, etc.). The early motivations for acceptingγ0as adjunctator were representation-dependent, mildly bearing relation to the actual conditions forcingγ0as adjunctator. Representation-independent approaches to the physical predictions of the Dirac equation are somewhat new, here presented as being the reasons forγ0as adjunctator of the Dirac theory, together with the essential role of the latter in the physical aspects of the theory.

Calculation of a divergence-free lamb shift

A divergence-free theory of the Lamb shift is presented, and calculations are carried out for hydrogen-like ions. The theory uses two Lorentz-invariant equations of motion, one for the electron in the presence of the photon, which is Dirac's four-space time-dependent equation, and the other for the photon in the presence of the electron. The electron–photon interaction is calculated from the Dirac current. The distribution of photon frequencies is bounded by the distribution of electron frequencies intrinsic to the Dirac current, thereby guaranteeing a divergence-free result for the Lamb shift. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Understanding quantum interference in general nonlocality

In this paper we attempt to give a new understanding of quantum double-slit interference of fermions in the framework of general nonlocality (GN) [J. Math. Phys. 49, 033513 (2008)] by studying the self-(inter)action of matter wave. From the metric of the GN, we derive a special formalism to interpret the interference contrast when the self-action is perturbative. According to the formalism, the characteristic of interference pattern is in agreement with experiment qualitatively. As examples, we apply the formalism to the cases governed by Schrödinger current and Dirac current, respectively, both of which are relevant to topology. The gap between these two cases corresponds to the fermion magnetic moment, which is possible to test in the near future. In addition, a general interference formalism for both perturbative and nonperturbative self-actions is presented. By analyzing the general formalism we predict that in the nonperturbative limit there is no interference at all. And by comparison with the special formalism of Schrödinger current, the coupling strength of self-action in the limit is found to be ∞. In the perturbative case, the interference from self-action turns out to be the same as that from the standard approach of quantum theory. Then comparing the corresponding coefficients quantitatively we conclude that the coupling strength of self-action in this case falls in the interval [0, 1].

Quantum molecular dynamics

Electron or ion dynamics are treated using spin-dependent quantum trajectories. These trajectories are inferred from the Dirac current, which contributes Schroedinger's current and additional spin-dependent terms, all of which are of order c0 in the nonrelativistic regime of particle velocity, where c is the speed of light. The many-body problem is treated precisely as in classical dynamics. Each electron or ion has its own equation of motion, which is the time-dependent Dirac or the time-dependent Schroedinger equation in the relativistic or nonrelativistic regime of particle velocity, respectively. As an example the theory is applied to the electronic structure of the helium atom, in which two electrons with opposite spin states are shown to correlate such that their quantum trajectories keep them on average on opposite sides of the nucleus. As the theory is time dependent, excited states are also generated. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Fully Relativistic Full-Potential Calculations of Magnetic Moments in Uranium Monochalcogenides with the Dirac Current

We study the orbital, spin, and total magnetic moments in uranium monochalcogenides, U X where X =S, Se, and Te, using the fully relativistic full-potential calculations based on the spin density functional theory. In particular, the orbital magnetic moments are calculated with the Dirac current. We employ two methods which adopt distinctly different basis sets; one is the fully relativistic full-potential linear-combination-of-atomic-orbitals (FFLCAO) method and the other is the fully relativistic full-potential mixed-basis (FFMB) method. Showing that the orbital magnetic moments calculated using the FFLCAO method and those calculated using the FFMB method agree very well with each other, we demonstrate that, in contrast to the conventional method, the method with the Dirac current enables us to calculate the orbital magnetic moments even if the basis set includes basis functions with no definite angular momenta, e.g., the plane waves in the FFMB method. Furthermore, it is found that the orbital magnetic...

About Twistor Spinors with Zero in Lorentzian Geometry

We describe the local conformal geometry of a Lorentzian spin manifold $(M,g)$ admitting a twistor spinor $\phi$ with zero. Moreover, we describe the shape of the zero set of $\phi$. If $\phi$ has isolated zeros then the metric $g$ is locally conformally equivalent to a static monopole. In the other case the zero set consists of null geodesic(s) and $g$ is locally conformally equivalent to a Brinkmann metric. Our arguments utilise tractor calculus in an essential way. The Dirac current of $\phi$, which is a conformal Killing vector field, plays an important role for our discussion as well.

Imaginary Killing spinors on (2, n − 2)-manifolds

In this paper we prove that a (2, n − 2)-manifold admitting an imaginary Killing spinor with nontrivial Dirac current, is at least locally a codimension one warped product with a special warping function. Hence, a (2, 2)-manifold admitting such an imaginary Killing spinor is Einstein iff it is conformally flat.

Spinor Derivation of Quasilocal Mean Curvature Mass in General Relativity

A spinor derivation is presented for quasilocal mean-curvature mass of spacelike 2-surfaces in General Relativity. The derivation is based on the Sen-Witten spinor identity and involves the introduction of novel nonlinear boundary conditions related to the Dirac current of the spinor at the 2-surface and the tangential flux of a boundary Dirac operator, as well the use of a spin basis adapted to the mean curvature frame of the 2-surface normal space. This setting may provide an alternative approach to a positivity proof for mean-curvature mass based on showing that Witten’s equation admits a spinor solution satisfying the proposed nonlinear boundary conditions.