Dirac Sea Research Articles

Chiral Soliton Models and Nucleon Structure Functions

We outline and review the computations of polarized and unpolarized nucleon structure functions within the bosonized Nambu-Jona-Lasinio chiral soliton model. We focus on a consistent regularization prescription for the Dirac sea contribution and present numerical results from that formulation. We also reflect on previous calculations on quark distributions in chiral quark soliton models and attempt to put them into perspective.

Physics Formalism Helmholtz Iyer Markoulakis Hamiltonian Mechanics Metrics towards Electromagnetic Gravitational Hilbert Coulomb Gauge String metrics

Iyer Markoulakis Helmholtz Hamiltonian metrics have been gauged to Coulombic Hilbert metrics, representing Gilbertian and Amperian natures of electromagnetic fields from mechanics of vortex rotational fields acting with gradient fields, typically in zero-point microblackhole general fields, extending to vacuum gravitational fields gauge. This ansatz general gaging helps to properly isolate field effects with physical analyses – mechanical, electric, magnetic components within the analytical processes. Vacuum gravitational fields and the flavor Higgs-Boson matter inertial gravitational fields have been thus quantified extending to stringmetrics constructs matrix showing charge asymmetry gauge metrics. Physical Analysis with applications to particle physics, Quantum ASTROPHYSICS, as well as grand unification physics have been advanced. Particle physics gauge matrix pointing to Dirac seas of electrons, monopoles with positrons, electron-positron annihilation leading to energy production, and the relativistic energy generating matter provided literature correlations. Quantum astrophysics extending gauge metrix analyzes of superluminal profile of signals velocity generating electron-positron chain like “curdling” action validates formalism with physics literature of electron-photon observed oscillatory fields configurations. Mechanism of creation of neutrino antineutrino pair orthogonal to electron positron “curdling” planes, that may lead to formation of protonic hydrogen of stars or orthogonally muon particles. These proposals will help to explain receding or fast expanding universe with the dark matter in terms of flavor metrics versus gauge associating metrics fields. Vacuum and gravitational monopoles, that are representation of compressed mass out of vortex Helmholtz decomposition fields have been interpolated to energy generation via electron positron monopole particles at cosmos extent of infinity

Chiral Anomaly, Dirac Sea and Berry monopole in Wigner Function Approach

Within Wigner function formalism, the chiral anomaly arises naturally from the Dirac sea contribution in un-normal-ordered Wigner function. For massless fermions, the Dirac sea contribution behaves like a 4-dimensional or 3-dimensional Berry monopole in Euclidian momentum space, while for massive fermions, although Dirac sea still leads to the chiral anomaly but there is no genuine Berry monopole. We discuss these points explicitly in a simple and concrete example.

Supersymmetry and Stable Dirac Sea in Carbon Nanotubes

We consider the construction of exactly solvable models of twisted carbon nanotubes by applying Darboux transformation to the square of the Dirac-like Hamiltonian, describing the low-energy dynamics of charge carriers. It is shown that obtained two pseudo-Schrodinger expressions are intertwined, demonstrating supersymmetry structure. It is proved, that for the considered class of pseudo-scalar external perturbations, the unitary disentanglement of negative/ positive states as within Foldy-Wouthuysen (FW) approach, so by Eriksen or SU(2) methods, can be carried out exactly, thus demonstrating the stability of the Dirac sea. The necessity of introduction of the probability density operator into the theory, while considering the problem in FW representation, is underlined.

On the Mathematical Foundations of Causal Fermion Systems in Minkowski Space

The emergence of the concept of a causal fermion system is revisited and further investigated for the vacuum Dirac equation in Minkowski space. After a brief recap of the Dirac equation and its solution space, in order to allow for the effects of a possibly nonstandard structure of spacetime at the Planck scale, a regularization by a smooth cutoff in momentum space is introduced, and its properties are discussed. Given an ensemble of solutions, we recall the construction of a local correlation function, which realizes spacetime in terms of operators. It is shown in various situations that the local correlation function maps spacetime points to operators of maximal rank and that it is closed and homeomorphic onto its image. It is inferred that the corresponding causal fermion systems are regular and have a smooth manifold structure. The cases considered include a Dirac sea vacuum and systems involving a finite number of particles and antiparticles.

Local algebras for causal fermion systems in Minkowski space

A notion of local algebras is introduced in the theory of causal fermion systems. Their properties are studied in the example of the regularized Dirac sea vacuum in Minkowski space. The commutation relations are worked out, and the differences to the canonical commutation relations are discussed. It is shown that the spacetime point operators associated to a Cauchy surface satisfy a time slice axiom. It is proven that the algebra generated by operators in an open set is irreducible as a consequence of Hegerfeldt's theorem. The light cone structure is recovered by analyzing expectation values of the operators in the algebra in the limit when the regularization is removed. It is shown that every spacetime point operator commutes with the algebras localized away from its null cone, up to small corrections involving the regularization length.

Plunging in the Dirac sea using graphene quantum dots

The dynamics of low energy charge carriers in a graphene quantum dot subjected to a time-dependent local field is investigated numerically. In particular, we study a configuration where a Coulomb electric field is provided by an ion traversing the graphene sample. A Galerkin-like numerical scheme is introduced to solve the massless Dirac equation describing charge carriers subjected to space- and time-dependent electromagnetic potentials and is used to evaluate the field induced interband transitions. It is demonstrated that as the ion goes through graphene, electron-hole pairs are generated dynamically via the adiabatic pair creation mechanism around avoided crossings, similar to electron-positron pair generation in low energy heavy ion collisions.

Fermion number 1/2 of sphalerons and spectral mirror symmetry

We present a rederivation of the baryon and lepton numbers frac{1}{2} of the SU(2)_L S sphaleron of the standard electroweak theory based on spectral mirror symmetry. We explore the properties of a fermionic Hamiltonian under discrete transformations along a noncontractible loop of field configurations that passes through the sphaleron and whose endpoints are the vacuum. As is well known, CP transformation is not a symmetry of the system anywhere on the loop, except at the endpoints. By augmenting CP with a chirality transformation, we observe that the Dirac Hamiltonian is odd under the new transformation precisely at the sphaleron, and this ensures the mirror symmetry of the spectrum, including the continua. As a consistency check, we show that the fermionic zero mode presented by Ringwald in the sphaleron background is invariant under the new transformation. The spectral mirror symmetry which we establish here, together with the presence of the zero mode, are the two necessary conditions whence the fermion number frac{1}{2} of the sphaleron can be inferred using the reasoning presented by Jackiw and Rebbi or, equivalently, using the spectral deficiency frac{1}{2} of the Dirac sea. The relevance of this analysis to other solutions is also discussed.

An Equation of State for Magnetized Neutron Star Matter and Tidal Deformation in Neutron Star Mergers

Abstract We derive an equation of state (EOS) for magnetized charge-neutral nuclear matter relevant for a neutron star (NS). The calculations are performed within an effective chiral model based on the generalization of the σ model with nonlinear self-interactions of the σ mesons along with the ρ−σ cross-coupling term. This model is extended by introducing the contributions of a strong magnetic field on the charged particles. The contributions arising from the effects of the magnetic field on the Dirac sea of charged baryons are also included. The resulting EOS for the magnetized dense matter is used to investigate the NS properties like its mass, radius, and tidal deformability. The magnitude of the magnetic field at the core of the NS considered here is in the range of 1015–1018 G, for which the relative deformation from spherical symmetry turns out to be less than 1%, giving a post facto justification for the spherically symmetric treatment of the NS structure. The dimensionless tidal deformability Λ1.4 is 526 for an NS with mass 1.4 M ⊙, which is consistent with the recent observation of GW 170817. The maximum mass of the NS in the presence of a strong magnetic field is consistent with the observational constraints on the mass of the pulsar PSR J0348–0432, and its radius at a mass of 1.4 M ⊙ is also in agreement with the empirical bounds.

A gauge fixing procedure for causal fermion systems

Causal fermion systems incorporate local gauge symmetry in the sense that the Lagrangian and all inherent structures are invariant under local phase transformations of the physical wave functions. In the present paper, it is explained and worked out in detail that, despite this local gauge freedom, the structures of a causal fermion system give rise to distinguished gauges where the local gauge freedom is fixed completely up to global gauge transformations. The main method is to use spectral and polar decompositions of operators on Hilbert spaces and on indefinite inner product spaces. We also introduce and make use of a Riemannian metric, which is induced on the manifold of all regular correlation operators by the Hilbert–Schmidt scalar product. Gaussian coordinate systems corresponding to this Riemannian metric are constructed. Moreover, we work with so-called wave charts where the physical wave functions are used as coordinates. Our constructions and results are illustrated in the example of Dirac sea configurations in finite and infinite spatial volume.

Resolving rapidly chirped external fields with Dirac vacuum

We study the dynamical response of the Dirac vacuum state to a very strong time-dependent electric field pulse, whose frequency is chirped in time. The resulting field-induced electron-positron pair-creation process can be used to examine various proposals for time-dependent frequency spectra of the external field. It turns out that the Dirac vacuum can be used as sensitive probe that can respond to the instantaneous values of the frequency at each moment of time by producing electrons with a characteristic energy. This almost instantaneous response feature of the vacuum state permits us to introduce a generalized rate equation. It is based on the concept of a time-dependent decay rate and can provide semianalytical solutions to predict the number of created electron-positron pairs during the interaction with arbitrarily chirped electric field pulses.

Real Time Dynamics and Confinement in the Zn Schwinger-Weyl lattice model for 1+1 QED

We study the out-of-equilibrium properties of 1+1 dimensional quantum electrodynamics (QED), discretized via the staggered-fermion Schwinger model with an Abelian Zn gauge group. We look at two relevant phenomena: first, we analyze the stability of the Dirac vacuum with respect to particle/antiparticle pair production, both spontaneous and induced by an external electric field; then, we examine the string breaking mechanism. We observe a strong effect of confinement, which acts by suppressing both spontaneous pair production and string breaking into quark/antiquark pairs, indicating that the system dynamics displays a number of out-of-equilibrium features.

Dirac sea and chiral anomaly in the quantum kinetic theory

We revisit the chiral anomaly in the quantum kinetic theory in the Wigner function formalism under the background field approximation. Our results show that the chiral anomaly is actually from the Dirac sea or the vacuum contribution in the un-normal-ordered Wigner function. We also demonstrate that this contribution modifies the chiral kinetic equation for antiparticles.

Circuit complexity for free fermion with a mass quench

By using a recent approach proposed by Hackl et al. to evaluate the complexity of the free fermionic Gaussian state, we compute the complexity of the Dirac vacuum state of the Fermi system with a mass quench. First of all, we review the counting method given by Hackl et al., and demonstrate that the result can be adapted to all of the compact transformation group G. Then, we utilize this result to study the time evolution of the complexity of these states. We show that, for the rotational invariant reference state, the total complexity of the incoming vacuum state will saturate the value of the instantaneous vacuum state at the late times, with a typical timescale to achieve the final stable state. Moreover, we find that the complexity growth under the sudden quench is directly proportional to the mass difference. And all of the results show some similar behaviors with the circuit complexity of Thermofield double states.

Transition between coherent and incoherent chirping mechanisms in electron-positron pair creation

We examine the effect of a frequency-chirped external force field on the final energy that has been absorbed by two classical mechanical oscillators, by quantum mechanical two- and three-level systems, and by electron-positron pairs that were created from the quantum field theoretical Dirac vacuum. By comparing the final dynamical responses to the original force field with that associated with the corresponding time-reversed field, we can test the sensitivity of each of these five systems to the temporal phase information contained in the field. We predict that the linear oscillator, the two-level atom, and the pair-creation process triggered by a spatially homogeneous field are remarkably immune to this phase, whereas the quartic oscillator, the three-level atom, or the pair-creation process caused by a space-time field absorb the provided energy differently depending on the temporal details of the external field.

Enhancement of pair creation due to locality in bound-continuum interactions

Electron-positron pair production from vacuum is studied in combined background fields, a binding electric potential well and a laser field. The production process is triggered by the interactions between the bound states in the potential well and the continuum states in the Dirac sea. By tuning the binding potential well, the pair production can be strongly affected by the locality of the bound states. The narrower bound states in position space are more efficient for pair production. This is in contrast to what is commonly expected that the wider extended bound states have larger region to interact with external fields and would thus create more particles. This surprise can be explained as the more localized bound states have a much wider extension in the momentum space, which can enhance the bound-continuum interactions in the creation process. This enhancement manifests itself in both perturbative and non-perturbative production regimes.

Vacuum effects on the properties of nuclear matter under an external magnetic field

The effects of the Dirac sea of the nucleons are investigated within a covariant model of the hadronic interaction. We extend the usual Mean Field Approximation and present a procedure to deal with divergences which are proportional to polynomials on the magnetic field intensity. For this purpose a nucleon propagator is used which takes accounts of the full effect of the magnetic field as well as the presence of the anomalous magnetic moments of both protons and neutrons. We examine single particle properties and bulk thermodynamical quantities and conclude that within a reasonable range of densities and magnetic intensities the effects found are moderate.

Weyl systems: anomalous transport normally explained

The chiral kinetic theory is derived from exact spinor mean field equations without symmetry-breaking terms for large classes of SU(2) systems with spin-orbit coupling. The influence of the Wigner function's off-diagonal elements is worked out. The decoupling of the diagonal elements renormalizes the drift according to Berry connection which is found as an expression of the meanfield, spin-orbit coupling and magnetic field. As special limit, Weyl systems are considered. The anomalous term $\sim\V E\V B$ in the balance of the chiral density appears consequently by an underlying conserving theory. The experimental observations of this term and the anomalous magneto-transport in solid-sate physics usually described by chiral kinetic theory are therefore not a unique signal for mixed axial-gravitational or triangle anomaly and no signal for the breaking of Lorentz-invariance. The source of the anomalous term is by two thirds the divergence of Berry curvature at zero momentum which can be seen as Dirac monopole and by one third the Dirac sea at infinite momentum. During the derivation of the chiral kinetic theory this source by the Dirac sea is transferred exclusively to the Dirac monopole due to the projection of the spinor Wigner functions to the chiral basis. The dynamical result is shown to suppress the anomalous term by two thirds.

Sauter–Schwinger effect with a quantum gas

The creation of particle–antiparticle pairs from vacuum by a large electric field is at the core of quantum electrodynamics. Despite the wide acceptance that this phenomenon occurs naturally when electric field strengths exceed Ec ≈ 1018 V m−1, it has yet to be experimentally observed due to the limitations imposed by producing electric fields at this scale. The high degree of experimental control present in ultracold atomic systems allow experimentalists to create laboratory analogs to high-field phenomena. Here we emulated massive relativistic particles subject to large electric field strengths, thereby quantum-simulated particle–antiparticle pair creation, and experimentally explored particle creation from ‘the Dirac vacuum’. Data collected from our analog system spans the full parameter regime from low applied field (negligible pair creation) below the Sauter–Schwinger limit, to high field (maximum rate of pair creation) far in excess of the Sauter–Schwinger limit. In our experiment, we perform direct measurements on an analog atomic system and show that this high-field phenomenon is well-characterized by Landau–Zener tunneling, well known in the atomic physics context, and we find full quantitative agreement with theory with no adjustable parameters.

Nucleon structure functions from the NJL-model chiral soliton

We present numerical simulations for unpolarized and polarized structure functions in a chiral soliton model. The soliton is constructed self-consistently from quark fields from which the structure functions are extracted. Central to the project is regularizing the Dirac sea (or vacuum) contribution to structure functions directly from the regularized action functional that defines the model. In turn, the structure functions are obtained from matrix elements of symmetry currents without assumptions on the nature of quark bilocal and bilinear operators. We discuss in detail how sum rules are realized at the level of the quark wave-functions in momentum space. The comparison with experimental data is convincing for the polarized structure functions but exhibits some discrepancies in the unpolarized case. The vacuum contribution to the polarized structure functions is particularly small.