Charged Massless Fermions Research Articles

Quantum theory of synchrotron radiation from charged massless fermions

Quantum theory of synchrotron radiation from charged massless fermions

Helical separation effect and helical heat transport for Dirac fermions

An ensemble of massless fermions can be characterized by its total helicity charge given by the sum of axial charges of particles minus the sum of axial charges of antiparticles. We show that charged massless fermions develop a dissipationless flow of helicity along the background magnetic field. We dub this transport phenomenon as the Helical Separation Effect (HSE). Contrary to its chiral cousin, the Chiral Separation Effect, the HSE produces the helical current in a neutral plasma in which all chemical potentials vanish. In addition, we uncover the Helical Magnetic Heat Effect which generates a heat flux of Dirac fermions along the magnetic field in the presence of non-vanishing helical charge density. We also discuss possible hydrodynamic modes associated with the HSE in neutral plasma.

Traversable wormholes in four dimensions

We present a wormhole solution in four dimensions. It is a solution of an Einstein Maxwell theory plus charged massless fermions. The fermions give rise to a negative Casimir-like energy, which makes the wormhole possible. It is a long wormhole that does not lead to causality violations in the ambient space. It can be viewed as a pair of entangled near extremal black holes with an interaction term generated by the exchange of fermion fields. The solution can be embedded in the Standard Model by making its overall size small compared to the electroweak scale.

Towards traversable wormholes from force-free plasmas

The near-horizon region of magnetically charged black holes can have very strong magnetic fields. A useful low-energy effective theory for fluctuations of the fields, coupled to electrically charged particles, is force-free electrodynamics. The low energy collective excitations include a large number of Alfven wave modes, which have a massless dispersion relation along the field worldlines. We attempt to construct traversable wormhole solutions using the negative Casimir energy of the Alfven wave modes, analogously to the recent construction using charged massless fermions. The behaviour of massless scalars in the near-horizon region implies that the size of the wormholes is strongly restricted and cannot be made large, even though the force free description is valid in a larger regime.

Radiative effects in two-dimensional models of quantum electrodynamics in a constant magnetic field

The radiative energy shift of an electron in a constant magnetic field has been considered in the framework of the ($2+1$)-dimensional quantum electrodynamics with four-component fermions as well as in reduced ${\mathrm{QED}}_{3+1}$ in which photons propagate in a ($3+1$)-dimensional bulk and fermions are localized on a 2-brane. Analytical expressions are obtained for the energy of interaction of the electron spin with an external field and the radiative shift of the electron mass after averaging over the spin states of the electron. For ultrarelativistic energies of an electron and relatively weak magnetic fields, the total probability of a photon emission by a massive electron and the anomalous magnetic moment of an electron in a reduced ${\mathrm{QED}}_{3+1}$ are calculated. The dependence of the obtained values on the invariant dynamic parameter of synchrotron radiation is investigated. The total probabilities of synchrotron radiation of a charged massless fermion and the production of a pair of charged massless fermions by a photon in an external magnetic field are calculated in ($2+1$)-dimensional models of quantum electrodynamics.

On the creation of charged massless fermion pair by a photon in an external constant uniform magnetic field in 2+1 dimensions

Creation of charged massless fermion pair by a photon in a constant uniform magnetic field is considered in the one-loop approximation of the [Formula: see text]-dimensional quantum electrodynamics (QED[Formula: see text]). We calculate the elastic scattering amplitude (EAS) of photon using the polarization operator of photon in the above magnetic field obtained earlier in our work. We analyze the elastic scattering amplitude of photon at various values of the photon energy and magnetic field strength. Very simple analytical formulas for EAS of photon are obtained in the so-called quasi-classical region. In the massive quantum electrodynamics the elastic scattering amplitude of photon defines its “mass” squared in the presence of external electromagnetic field and the imaginary part of EAS describes the total probability of charged massive fermion pair creation in the electromagnetic field; we assume that it is the case and in the massless quantum electrodynamics.

Radiative dynamical mass of planar charged fermion in a constant homogeneous magnetic field

The effective Lagrangian and mass operator are calculated for planar charged massive and massless fermions in a constant external homogeneous magnetic field in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED_{2+1}). We obtain the renormalizable effective Lagrangian and the fermion mass operator for a charged fermion of mass m and then calculate these quantities for the massless case. The radiative corrections to the mass of charged massless fermion when it occupies the lowest Landau level are found for the cases of the pure QED_{2+1} as well as the so-called reduced QED_{3+1} on a 2-brane. The fermion masses were found can be generated dynamically in an external magnetic field in the pure QED_{2+1} if the charged fermion has small bare mass m_0 and in the reduced QED_{3+1} on a 2-brane even at m_0=0. The dynamical mass seems to be likely to be revealed in monolayer graphene in the presence of constant homogeneous magnetic field (normal to the graphene sample).

Consistent relativistic chiral kinetic theory: A derivation from on-shell effective field theory

We formulate the on-shell effective field theory (OSEFT) in an arbitrary frame and study its reparametrization invariance (RI), which ensures that it is respectful of Lorentz symmetry. In this formulation the OSEFT Lagrangian looks formally equivalent to the sum over light-like velocities of soft collinear effective field theory in the Abelian limit, differences remain in the scale of the gauge fields involved in the two effective theories. We then use the OSEFT Lagrangian expanded in powers of the on-shell energy to derive how the classical transport equations for charged massless fermions are corrected by quantum effects, as derived from quantum field theory. We provide a formulation in a full covariant way, and explain how the consistent form of the chiral anomaly equation can be recovered from our results. We also show how the side jump transformation of the distribution function associated with massless charged fermions can be derived from the RI transformation rules of the OSEFT quantum fields. Finally, we discuss differences in our results with others found in the literature.

Vacuum polarization of planar charged fermions with Coulomb and Aharonov–Bohm potentials

Vacuum polarization of charged massless fermions is investigated in the superposition of Coulomb and Aharonov–Bohm (AB) potentials in 2 + 1 dimensions. For this purpose, we construct the Green function of the two-dimensional Dirac equation with Coulomb and AB potentials (via the regular and irregular solutions of the radial Dirac equation) and then calculate the vacuum polarization charge density in the so-called subcritical and supercritical regimes. In the supercritical regime, the Green function has a discontinuity in the complex plane of “energy” due to the singularities on the negative energy axis; these singularities are situated on the unphysical sheet and related to the creation of infinitely many quasistationary fermionic states with negative energies. We expect that our results will be helpful in gaining deeper understanding of the fundamental problem of quantum electrodynamics which can be applied to the problems of charged impurity screening in graphene taking into consideration the electron spin.

Berry phase and anomalous velocity of Weyl fermions and Maxwell photons

We consider two systems of wave equations whose wave packet solutions have trajectories that are altered by the “anomalous velocity” effect of a Berry curvature. The first is the matrix Weyl equation describing cyclotron motion of a charged massless fermion. The second is Maxwell equations for the whispering-gallery modes of light in a cylindrical waveguide. In the case of the massless fermion, the anomalous velocity is obscured by the contribution from the magnetic moment. In the whispering-gallery modes, the anomalous velocity causes the circumferential light ray to creep up the cylinder at the rate of one wavelength per orbit, and can be identified as a continuous version of the Imbert–Federov effect.

Duality between zeroes and poles in holographic systems with massless fermions and a dipole coupling

We discuss the zeroes and poles of the determinant of the retarded Green function ($\det G_R$) at zero frequency in a holographic system of charged massless fermions interacting via a dipole coupling. For large negative values of the dipole coupling constant $p$, $\det G_R$ possesses only poles pointing to a Fermi liquid phase. We show that a duality exists relating systems of opposite $p$. This maps poles of $\det G_R$ at large negative $p$ to zeroes of $\det G_R$ at large positive $p$, indicating that the latter corresponds to a Mott insulator phase. This duality suggests that the properties of a Mott insulator can be studied by mapping the system to a Fermi liquid. Finally, for small values of $p$, $\det G_R$ contains both poles and zeroes (pseudo-gap phase).

Charge exchange scattering of higher partial-wave fermions by a Julia-Zee dyon

The Dirac equation in the field of an extended SU(2) dyon is studied for a massless fermion isodoublet with nonzero angular momentum J. The scattering amplitudes for all partial waves are obtained, and the dependence on the energy and the dyon's charge are explicitly given. Because the Coulomb potential of a dyon in the time independent gauge does not vanish at large distances, the asymptotic kinetic energy of a positively and negatively charged massless fermion E ± does not coincide with the energy E, the eigenvalue of the Dirac hamiltonian. In the limit of small dyon radius and electric charge, the charge exchange scattering amplitude can be parametrized by a suppression factor ∣4 E + E − r 0 2∣√ J( J+1) = ∣( eq/4 π) 2 − (2 Er 0) 2∣√ J( J+1) where e is the SU(2) gauge coupling constant, q is the electric charge of the dyon, and r 0 is the “radius” of the dyon. For sufficiently low energies E, this amplitude is only suppressed by powers of eq 4π . However, a dyon radiates away electric charge through fermion pairs. When the self-consistency requirement is imposed that the overall charge conservation holds for the combined dyon-fermion system, the dyon can only have a very small charge and E + ∼ E − ∼ E. Consequently, the charge exchange scattering found in the external field problem becomes completely negligible for low-energy fermions with J ⩾ 1. Therefore, the only physically significant charge exchange scattering is that of the s-wave fermions. The details are given for a specific model (which we call the asymptotic model) in which the dyon has a sharp edge: the exterior potentials are approximated by their asymptotic forms, while the interior potentials are replaced by their values at the origin. In an appendix we show that our result is quite general, and the dependence on a particular dyon potential used is characterized by a numerical factor of order unity.

Anomalies and the particle content of grand unified theories

For the largest class of grand unified models based on simple gauge groups, the presence of anomalies not only results in unrenormalizability, but in addition means that there are charged, massless fermions in the theory. Conversely, the absence of charged, massless particles in such models guarantees the absence of anomalies. For models outside this class, if there are anomalies but no charged massless fermions, the anomalies occur only for rather exotic currents.

Infrared problem and boson suppression in massless Abelian gauge theory

The vacuum polarization effects lead to a complete shielding of the charge and to a suppression of real boson excitations in massless Abelian gauge theory. Nevertheless, fermions interact by means of neutral vector currents. It is concluded that charged massless fermions cannot exist.

Renormalization group and superconductivity, and neutrino-type solutions in field theory

The Bogoliubov-Shirkov differential equations for the renormalization group are modified to investigate the dynamical mechanism of mass generation in field theory. It is shown that in quantum electrodynamics with cut-off, a fermion may acquire a superconductivity-type mass only if the bare coupling constant α Λ exceeds some critical value α C. When α Λ < α C, the fermion remains massless. The vacuum polarization of massless fermions leads to a complete shielding of the bare charge (neutrino-type solution). As a result, it is concluded that charged massless fermions cannot exist.

An electrodynamic approach to the electron-muon mass ratio

By a mechanism well known from the theory of superconductivity the particles of an electrically charged massless fermion field may obtain a nonvanishing rest mass. If the mass renormalization in ordinary quantum electrodynamics is infinite, then it seems likely that a proper reformulation of the basic equations of quantum electrodynamics which eliminates the infinite constant δm will be a dilatationally-invariant theory corresponding to the model above. The dilatation invariance of the basic theory is not objectionable and opens on the contrary a natural possibility to understand how two leptons can have almost identical interactions but vastly different masses. The mass of a lepton is then determined by the nondilatationally-invariant perturbation caused by the other charged fields present in nature.