Search Results (11)

A new non-minimal version of the Einstein–Dirac-axion theory is established. This version of the non-minimal theory describing the interaction of gravitational, spinor, and axion fields is of the second order in derivatives in the context of the Effective Field Theory and is of the first order in the spinor particle number density. The model Lagrangian contains four parameters of non-minimal coupling and includes, in addition to the Riemann tensor, Ricci tensor, and Ricci scalar, as well as left-dual and right-dual curvature tensors. The pseudoscalar field appears in the Lagrangian in terms of trigonometric functions providing the discrete symmetry associated with axions, which is supported. The coupled system of extended master equations for the gravitational, spinor, and axion fields is derived; the structure of new non-minimal sources that appear in these master equations is discussed. Application of the established theory to the isotropic homogeneous cosmological model is considered; new exact solutions are presented for a few model sets of guiding non-minimal parameters. A special solution is presented, which describes an exponential growth of the spinor number density; this solution shows that spinor particles (massive fermions and massless neutrinos) can be born in the early Universe due to the non-minimal interaction with the spacetime curvature. Full article

Although electrons (fermions)and photons (bosons) produce the same interference patterns in the two-slit experiments, known in optics for photons since the 17th Century, the description of these patterns for electrons and photons thus far was markedly different. Photons are spin one, relativistic and massless particles while electrons are spin half massive particles producing the same interference patterns irrespective to their speed. Experiments with other massive particles demonstrate the same kind of interference patterns. In spite of these differences, in the early 1930s of the 20th Century, the isomorphism between the source-free Maxwell and Dirac equations was established. In this work, we were permitted replace the Born probabilistic interpretation of quantum mechanics with the optical. In 1925, Rainich combined source-free Maxwell equations with Einstein’s equations for gravity. His results were rediscovered in the late 1950s by Misner and Wheeler, who introduced the word "geometrodynamics” as a description of the unified field theory of gravity and electromagnetism. An absence of sources remained a problem in this unified theory until Ranada’s work of the late 1980s. However, his results required the existence of null electromagnetic fields. These were absent in Rainich–Misner–Wheeler’s geometrodynamics. They were added to it in the 1960s by Geroch. Ranada’s solutions of source-free Maxwell’s equations came out as knots and links. In this work, we establish that, due to their topology, these knots/links acquire masses and charges. They live on the Dupin cyclides—the invariants of Lie sphere geometry. Symmetries of Minkowski space-time also belong to this geometry. Using these symmetries, Varlamov recently demonstrated group-theoretically that the experimentally known mass spectrum for all mesons and baryons is obtainable with one formula, containing electron mass as an input. In this work, using some facts from polymer physics and differential geometry, a new proof of the knotty nature of the electron is established. The obtained result perfectly blends with the description of a rotating and charged black hole. Full article

In this paper, we obtain the metric of the space-time generated by a charged and rotating gravitational body surrounded by a loud of strings, namely, the Kerr–Newman black hole space-time with the addition of a cloud of strings. In this background, we find the radial solutions of the Dirac equation for massive particles and show that they are given in terms of the Generalized Heun functions. The dependence of these solutions on the parameter that codifies the presence of the cloud of strings is pointed out. Full article

We study the particle creation process in the Schwinger model coupled with an external classical source. One can approach the problem by taking advantage of the fact that the full quantized model is solvable and equivalent to a (massive) gauge field with a non-local effective action. Alternatively, one can also face the problem by following the standard semiclassical route. This means quantizing the massless Dirac field and considering the electromagnetic field as a classical background. We evaluate the energy created by a generic, homogeneous, and time-dependent source. The results match exactly in both approaches. This proves in a very direct and economical way the validity of the semiclassical approach for the (massless) Schwinger model, in agreement with a previous analysis based on the linear response equation. Our discussion suggests that a similar analysis for the massive Schwinger model could be used as a non-trivial laboratory to confront a fully quantized solvable model with its semiclassical approximation, therefore mimicking the long-standing confrontation of quantum gravity with quantum field theory in curved spacetime. Full article

It is argued that from a formal point of view, the classical limit of light quanta or photons is not that of a point-like particle but that of a geometric ray. According to this view, standard particle-wave dualism, which is often used in schools to describe the quantum behavior of massive objects, could be replaced by a ray-wave dualism (or even a particle-ray-wave trialism), which seems to be more appropriate for massless quantum objects such as photons. We compare the limits leading from quantum electrodynamics to a classical (Hamiltonian) theory of particles for electrons with those leading from photons via Maxwell’s equations to geometric ray optics. We also discuss the question to which extent Maxwell’s theory for electromagnetic waves should be considered as being on the same formal level as Schrödinger’s or Dirac’s theory. Full article

Ultra-high energy (UHE) photons with energies exceeding ${10}^{18}\mathrm{eV}$ can potentially be observed. They are produced in various processes involving electrically charged particles. However, more exotic scenarios are also possible. UHE photons could be emitted in encounters of massive magnetically charged monopole-antimonopole pairs or in processes associated with monopoles accelerated to high energies, typically ${10}^{21}\mathrm{eV}$ or beyond. Observing UHE photons can pose constraints on the properties of magnetic monopoles. There are compelling theoretical reasons in favor of the presence of magnetic monopoles in nature. The predicted observational signatures of these particles are therefore searched for in dedicated experiments currently in operation. Despite these attempts, magnetic monopoles have yet to be empirically proved. There are also theoretical reasons why magnetic monopoles allowed by Dirac’s theory might not be realized in nature in the form of isolated particles. Detection or non-detection of UHE photon signatures of magnetic monopoles would bring us closer to solving this fascinating puzzle. Full article

Dirac bispinors belong to an irreducible representation of the complete Lorentz group, which includes parity as a symmetry yielding two intrinsic discrete degrees of freedom: chirality and spin. For massive particles, chirality is not dynamically conserved, which leads to chiral oscillations. In this contribution, we describe the effects of this intrinsic structure of Dirac bispinors on the quantum entanglement encoded in a lepton-antineutrino pair. We consider that the pair is generated through weak interactions, which are intrinsically chiral, such that in the initial state the lepton and the antineutrino have definite chirality but their spins are entangled. We show that chiral oscillations induce spin entanglement oscillations and redistribute the spin entanglement to chirality-spin correlations. Such a phenomenon is prominent if the momentum of the lepton is comparable with or smaller than its mass. We further show that a Bell-like spin observable exhibits the same behavior of the spin entanglement. Such correlations do not require the knowledge of the full density matrix. Our results show novel effects of the intrinsic bispinor structure and can be used as a basis for designing experiments to probe chiral oscillations via spin correlation measurements. Full article

Monopole solutions in SU(2) Yang–Mills theory, which interact with massive nonlinear spinor fields, described by the nonlinear Dirac equation, are obtained. These solutions describe a magnetic monopole created by a spherical lump of nonlinear spinor fields. It is shown that the monopole solutions obtained differ in principle from the ‘t Hooft–Polyakov monopole so that (a) it is topologically trivial; (b) the radial magnetic field decreases as $r^{-3}$; (c) the Higgs field is not necessary for its existence. It is demonstrated that the energy spectrum of such a system possesses a global minimum, the appearance of which is due exclusively to the nonlinearity of the Dirac spinor fields. This global minimum can be considered a mass gap, i.e., the energy difference between a vacuum and the next lowest energy state. A similar minimum was found for the energy spectrum of regular solutions to the nonlinear Dirac equation and this minimum is called “the lightest stable particle”. Full article

Are neutrinos with definite masses Majorana or Dirac particles? This is one of the most fundamental problems of modern neutrino physics. The solution to this problem could be crucial for understanding the origin of small neutrino masses. We review here basic arguments in favor of the Majorana nature of massive neutrinos. The phenomenological theory of $0\nu \beta \beta$-decay is briefly discussed and recent experimental data and sensitivity of future experiments are presented. Full article

Wigner’s little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take different mathematical forms for massive and for massless particles. However, it is shown possible to construct one unified representation using a graphical description. This graphical approach allows us to describe vividly parity, time reversal, and charge conjugation of the internal symmetry groups. As for the language of group theory, the two-by-two representation is used throughout the paper. While this two-by-two representation is for spin-1/2 particles, it is shown possible to construct the representations for spin-0 particles, spin-1 particles, as well as for higher-spin particles, for both massive and massless cases. It is shown also that the four-by-four Dirac matrices constitute a two-by-two representation of Wigner’s little group. Full article

The dynamical property of electrons with the tilted Dirac cone was examined using the tilted Weyl equation. The polarization function exhibits cusps and nonmonotonic structures by varying both the frequency and the momentum. A pair of tilted Dirac cones exhibits a new plasmon for the intermediate magnitude of momentum owing to the combined effects of two tilted cones. Dirac electrons with the zero-gap state (ZGS) in organic conductor α-(BEDT-TTF)₂I₃ are examined by calculating the Berry curvature, which displays the peak structure for a pair of Dirac particles between the conduction band and the valence band. The ZGS is theoretically predicted for α-(BEDT-TTF)₂NH₄Hg(SCN)₄ under uniaxial pressure. Examining the band structure of the stripe charge ordered state of α-(BEDT-TTF)₂I₃ under pressure, we have found a topological transition from a conventional insulator to a new phase of a pair of Dirac electrons with a finite mass. Further, investigating the zero-energy (N = 0) Landau level under a strong magnetic field, we propose ferromagnetism breaking the SU(2) valley-pseudo-spin symmetry, and the phase fluctuations of the order parameters leading to Kosterlitz-Thouless transition at lower temperatures. Full article