The magnetic moment of composite leptons and quarks

We show that for a composite fermion of sufficiently small radius, the magnetic moment approaches the Dirac value corresponding to the overall charge and mass, regardless of the constituent values. This resolves a recently suggested difficulty in composite models of leptons and quarks.     

Model building for a 17 KeV neutrino

We study models with Goldstone bosons (“triplet”-Majorons, familons and Majorons with singlet Higgs fields) accomodating the 17 KeV neutrino reported by Simpson. We consider the possibility of Dirac and Majorana neutrinos. In both cases all phenomenological bounds, includin that coming from “standard” galaxy formation models, are satisfied.     

The mass of the muon

It is shown that a classical relativistic charged particle has an anomalous magnetic moment g=4α/3. If such a “dressed” particle with its mass m, charge e, and anomalous magnetic moment g is quantized by a generalized Dirac equation, then the wave equation predicts a second mass m_μ=m_e(3/2α+1). It is suggested that a magnetic portion of the self-energy is quantized.     

Magnetic moments of composite fermions

There have been a considerable number of papers proposing composite models for leptons and quarks. Recently, Glück and Lipkin have stated that reproducing the observed magnetic moments of these fermions presents a serious difficulty for these composite models. We show for a renormalizable theory that, in contrast to Glück's and Lipkin's nonrelativistic arguments, a deeply bound system (with heavy constituent particle masses m_c) of (total) spin $\text{1}\text{2}$, charge e and mass m has the magnetic moment $\text{(e/2m) [1 +}\text{“usual” (QED + QCD + weak) corrections +O}\text{(m/m}{}_{\mathrm{<mtext>c</mtext>}}\text{)}\text{“new” bindng corrections]}$. Although there remains the considerable dynamical problem of obtaining “light” bound fermions from heavy constituents, there is no separate, additional magnetic moment difficulty.     

Artificial graphenes: Dirac matter beyond condensed matter

After the discovery of graphene and of its many fascinating properties, there has been a growing interest for the study of “artificial graphenes”. These are totally different and novel systems that bear exciting similarities with graphene. Among them are lattices of ultracold atoms, microwave or photonic lattices, “molecular graphene” or new compounds like phosphorene. The advantage of these structures is that they serve as new playgrounds for measuring and testing physical phenomena that may not be reachable in graphene, in particular the possibility of controlling the existence of Dirac points (or Dirac cones) existing in the electronic spectrum of graphene, of performing interference experiments in reciprocal space, of probing geometrical properties of the wave functions, of manipulating edge states, etc. These cones, which describe the band structure in the vicinity of the two connected energy bands, are characterized by a topological “charge”. They can be moved in the reciprocal space by appropriate modification of external parameters (pressure, twist, sliding, stress, etc.). They can be manipulated, created or suppressed under the condition that the total topological charge be conserved. In this short review, I discuss several aspects of the scenarios of merging or emergence of Dirac points as well as the experimental investigations of these scenarios in condensed matter and beyond.     

Nonlinear Spin and Pseudo-Spin Symmetric Dirac Equations

Nonlinear Dirac equations are obtained by variation of the spinor action whose Lagrangian components have the same conformal degree and the coupling parameter of the self-interaction term is dimensionless. In 1+1 space-time, we show that these requirements result in the “conventional” quartic form of the nonlinear interaction and present the general equation for various coupling modes. These include, but not limited to, the Thirring and Gross-Neveu models. We consider the spin and pseudo-spin symmetric models and obtain a numerical solution. We also propose a two-component “minimal” pseudo-scalar coupling model.     

Prequantum Classical Statistical Field Theory: Schrödinger Dynamics of Entangled Systems as a Classical Stochastic Process

The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a “quantum system” is just a label for (so to say “prequantum”) classical random field. Quantum averages can be represented as classical field averages. Correlations between observables on subsystems of a composite system can be as well represented as classical correlations. In particular, it can be done for entangled systems. Creation of such classical field representation demystifies quantum entanglement. In this paper we show that quantum dynamics (given by Schrödinger’s equation) of entangled systems can be represented as the stochastic dynamics of classical random fields. The “effect of entanglement” is produced by classical correlations which were present at the initial moment of time, cf. views of Albert Einstein.     

Magnetic-like field inducing negative Dirac mass in graphene on hexagonal boron nitride

The tight-binding electrons in graphene grown on top of hexagonal boron nitride (h-BN) substrate are studied. The two types of surfaces on the h-BN substrate give rise to Dirac fermions having positive and negative masses. The positive and negative masses of the Dirac fermions lead to the gapped graphene to behave as a “pseudo” ferromagnet. A very large (pseudo) tunneling magnetoresistance is predicted when the Fermi level approaches the gap region. The energy gap due to the breaking of sublattice symmetry in graphene on h-BN substrate is analogous to magnetic-induced energy gap on surface of topological insulators. We point out that positive and negative masses may correspond to signs of magnetic-like field perpendicular to graphene sheet acting on pseudo magnetic dipole moment of electrons, leading to pseudo-Larmor precession and Stern–Gerlach magnetic force.     

A class of “natural” composite models

The starting point is the attractive class of composite models where quarks and leptons appear as fermion-scalar bound states (Fφ). The aim is to resolve the “naturality” problem associated with fundamental scalars without losing the appealing properties of Fφ-type composite models. A systematic construction of such models is given, where the scalar constituents automatically qualify as light dynamical scalars, i.e. as composite (pseudo) Goldstonebosons. A comfortably large class of composite models then results, where all standard “naturality” requirements are satisfied: the quark and lepton masses are kept small through 't Hooft's chiral protection mechanism; the dynamical scalar “constituents” are light and the CP problem of QCD finds an automatic solution. Further characteristics are economy, absence of light exotics, possibility of three generations and elegance of anomaly matching. It is shown that existing attractive models with fundamental scalars can be made “natural” in the sense defined above.     

On the Chirality Quantum Phase Transition of the Dirac Oscillator

Dirac oscillator subjects to an external magnetic field is re-examined. We show that this model can be mapped onto different quantum optics models if one insists to introduce two kinds of phonons which associate with the excitations of Dirac oscillator and magnetic field respectively. The conclusion about chirality quantum phase transition in the paper “Chirality quantum phase transition in the Dirac oscillator” (Bermudez et al. Phys. Rev. A, 77, 063815 2008) is only valid for a specific mapped quantum optics models rather than the Dirac oscillator itself. Thus, the conclusions about chirality quantum phase transitions in this paper are not universal.     

The p-q model Boltzmann equation

The “p-q” model earlier introduced by the authors to describe persistent scattering under a scalar Boltzmann equation is here examined in detail. After deriving the scattering kernel and exhibiting its properties we obtain moment and similarity solutions and show how the model effectively parametrizes all intermediate conditions between the extremes of diffusion-like “small-scattering” and the strong-collisional limit of “diffuse-scattering” characteristic of earlier, more restrictive models. Both continuous and discrete-variable versions of the model are discussed and shown to be straightforwardly interrelated. Our derivations, carried out in natural energy-like variables, parallel those given recently by Ernst and Hendriks using transform methods.     

Spectral properties of reduced Bloch Hamiltonians

Bloch Hamiltonians are defined, and the existence of bands is proven for a large class of periodic operators. The results are strong enough to include most of the reasonable physical models of a single electron in crystals. A notable exception is the Dirac Bloch Hamiltonian for a Coulombic crystal with high charge. Properties of the Bloch waves are briefly described and it is shown that “simple” Bloch Hamiltonians do not have Bloch waves with a finite number of Fourier coefficients. The asymptotic distribution of the bands is determined, and it is shown that for a large class of Hamiltonians, it is determined by the kinetic energy alone.     

Noninertial Effects on a Dirac Neutral Particle Inducing an Analogue of the Landau Quantization in the Cosmic String Spacetime

We discuss the behavior of external fields interacting with a Dirac neutral particle with a permanent electric dipole moment in order to achieve relativistic bound state solutions in a noninertial frame and in the presence of a topological defect spacetime. We show that the noninertial effects of the Fermi?CWalker reference frame induce a radial magnetic field even in the absence of magnetic charges, which is influenced by the topology of the cosmic string spacetime. We then discuss the conditions that the induced fields must satisfy to yield the relativistic bound states corresponding to the Landau?CHe?CMcKellar?CWilkens quantization in the cosmic string spacetime. Finally, we obtain the Dirac spinors for positive-energy solutions and the Gordon decomposition of the Dirac probability current.     

Quantum radiation theory in a diffusion model version

Using the diffusion model associated by the author with the wave equations, a part of current quantum radiation theory is reformulated so that the characteristic divergences in the associated calculations no longer arise. The reformulation does this by stipulating, on purely physical grounds, that a transition involving a “virtual” quantum must include a high frequency “cutoff” factor in its interaction Hamiltonian. For a transition involving a “real” quantum, the stipulation is that the “cutoff” factor is not to be included.     

Quantenphysikalischer Ursprung der Eichidee

The Quantum Physical Origin of the Gauge Idea To consider quantum physics as an interplay of creation and annihilation processes has the consequence that gauge field theories are not only possible but necessary. Since the complex conjugate phase factors of each pair of fermion creators and annihilators can be arbitrary chosen, quantum field theories must be completely phase invariant. Unfortunately, even globally the Dirac equation for systems of free fermions is not phase invariant. The Dirac matrices are namely transformed, if we multiply the spinor components by different constant phase factors. The Dirac equations before and after the transformation are however physically equivalent. We may therefore say: Systems of free fermions will be completely described, only if we consider the class of all equivalent Dirac equations. Since Dirac's commutation relations are unitarily invariant, the class equivalent Dirac equations is invariant under all transformations of the group U 4. Unitary diagonal matrices yield arbitrary phase transformations. Hence, gauge fields of the group U 4 are compatible with the postulate of general phase invariance. These gauge file are so similar to the QED that we may speak of an “extended quantum electrodynamics”, EQE. Here, we will show that EQE exists. The invariant subgroup U 1 U 4 yields QED. The complementary subgroup SU 4 includes four subgroups SU 3, there subgroups O 4, and six subgroups SU 2. The latter ones may yield three pairs of quarks and three pairs of leptons, where the quarks form a group SU 3. More than two times three pairs of elementary fermions does not exist in in EQE Probably, EQE is different from the United EQD and QCD. However, it should be a promising version of a field theory in elementary particle physics, because it follows from an existing symmetry of the empirically wel founded Dirac theory. EQE is therefore free from hypothesis in the Newtonian sense of the word. Whatever it will finally mean, it cannot be rejected, since phase invariance must be required. The invention of new symmetries and the acception of a bie number of independent spinor components is dispensable or must be postponed at least.     

Zitterbewegung in Quantum Mechanics

The possibility that zitterbewegung opens a window to particle substructure in quantum mechanics is explored by constructing a particle model with structural features inherent in the Dirac equation. This paper develops a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. The model admits periodic solutions with quantized energy, and the correct magnetic moment is generated by charge circulation. It attributes to the electron an electric dipole moment rotating with ultrahigh frequency, and the possibility of observing this directly as a resonance in electron channeling is analyzed in detail. Correspondence with the Dirac equation is discussed. A modification of the Dirac equation is suggested to incorporate the rotating dipole moment.     

Electric dipole moment of Dirac fermionic dark matter

The direct limit of electric dipole moment and direct searches for dark matter by electric dipole interaction are investigated with including the electromagnetic nuclear form factor, in case that the dark matter candidate is a Dirac particle. The electric dipole moment of dark matter constrained by direct searches must be lower than 7×¹⁰−22e cm for dark matter mass of 100 GeV to satisfy the current experimental exclusion limits at XENON10 and CDMS II. The CP violation of electric dipole moment and the dark matter discovery by electric dipole interaction in the future are considered.