The spacetime of a Dirac fermion

We present an approximate solution to the minimally coupled Einstein-Dirac equations. We interpret the solution as describing a massive fermion coexisting with its own gravitational field. The solution is axisymmetric but is time dependent. The metric approaches that of a flat spacetime at the spatial infinity. We have calculated a variety of conserved quantities in the system.     

Superconductivity in the presence of fermion condensation

Fermion condensation (FC) is studied within the density functional theory. FC can fulfill the role of a boundary, separating the region of strongly interacting electron liquid from the region of strongly correlated electron liquid. Consideration of the superconductivity in the presence of FC shows that, under certain circumstances, at temperatures above T _c the superconductivity vanishes and the superconducting gap smoothly transforms into a pseudogap. The pseudogap occupies only a part of the Fermi surface, and one that shrinks with increasing temperature and vanishes at T=T*, and the single-particle excitations of the gapped area of the Fermi surface have a width γ ∼(T-T _c ). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 491–496 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Entanglement entropy for a Dirac fermion in three dimensions: Vertex contribution

In three dimensions there is a logarithmically divergent contribution to the entanglement entropy which is due to the vertices located at the boundary of the region considered. In this work we find the corresponding universal coefficient for a free Dirac field, and extend a previous work in which the scalar case was treated. The problem is equivalent to find the conformal anomaly in three-dimensional space where multiplicative boundary conditions for the field are imposed on a plane angular sector. As an intermediate step of the calculation we compute the trace of the Green function of a massive Dirac field in a two-dimensional sphere with boundary conditions imposed on a segment of a great circle.     

A spin observable for a Dirac particle

We discuss the form of the spin operator in relativistic quantum mechanics. We derive the form of the spin operator in the case when the states with negative energies are admitted. It appears that for a Dirac particle the spin operator reduces to the so called mean-spin operator introduced by Foldy and Wouthuysen. We show that the spin operator transforms under Lorentz group action according to an operator Wigner rotation, analogously as a Bloch vector describing polarization of a particle in momentum representation.     

Majorana mass of the electron-muon Dirac neutrino and the fermion masses

The left-handed electron and muon neutrinos are considered to be Majorana neutrinos with equal mass. They have oppositeCP parities and are equivalent to a single Dirac neutrino. These neutrinos are shown to have a Majorana mass of about 6.5 eV. The relatively large mass of their charged leptons is due to their γ₅ coupling with the Higgs scalars By expressing the Higgs scalars as Clebsch-Gordon type of combinations ofZ andD neutral vector bosons with appropriate quantum numbers, it is shown that 2m _e m _μ /(m _e ² +m _μ ² )=(g_{v/g A}) _eμ ² , whereg _v andg _A are the vector and axial vector coupling constants, respectively, ofZ (orD) with the leptonse and μ. Weinberg mixing parametersx _L =e²/g _L ² andx _R =e ²/g _R ² are determined to be 0.2254 and 0.2746, respectively. In the quark sector the Cabibbo angle is about 13°11′ and the masses oft andb quarks are found to be respectively 134.2 and 4.69 GeV.     

Muon spin relaxation in heavy fermion systems

Heavy fermion systems have received a great deal of study by a wide variety of techniques, includingSR. In a number of systems, coexisting superconducting and magnetic states have been reported, leading to speculation of an intimate connection between magnetism and superconductivity in these compounds. We observe a spontaneous magnetic field in the superconducting phase of UPt₃. In addition, the broadening of the transverse field muon precession signal only onsets approximately 60 mK below the superconductingT _c. Our results provide evidence that the lower superconducting phase in theH-T phase diagram of UPt₃ is characterised by broken time-reversal symmetry. Measurements of URu₂Si₂ and CeCu_2.2Si₂ indicate that the magnetically ordered volume fraction is temperature dependent in both systems.     

狄拉克理论中自旋矩阵的严格推导

证明了对于狄拉克理论中的自旋矩阵,通常给出的形式就是其一般形式,证明中不涉及具体表象.     

Slave fermion formalism for the tetrahedral spin chain

We use the SU(2) slave fermion approach to study a tetrahedral spin 1/2 chain, which is a one-dimensional generalization of the two dimensional Kitaev honeycomb model. Using the mean field theory, coupled with a gauge fixing procedure to implement the single occupancy constraint, we obtain the phase diagram of the model. We then show that it matches the exact results obtained earlier using the Majorana fermion representation. We also compute the spin-spin correlation in the gapless phase and show that it is a spin liquid. Finally, we map the one-dimensional model in terms of the slave fermions to the model of 1D p-wave superconducting model with complex parameters and show that the parameters of our model fall in the topological trivial regime and hence does not have edge Majorana modes.     

Dirac equation in the presence of a spatially periodic magnetic field

In the present article we separate variables in the Dirac equation in the presence of a spatially periodic magnetic field. We reduce the problem to solving a coupled system of first order differential equations. We show that the solution recently reported by Sen Gupta [7] is not correct.     

Semiclassical dynamics and transport of the Dirac spin

A semiclassical theory of spin dynamics and transport is formulated using the Dirac electron model. This is done by constructing a wavepacket from the positive-energy electron band, and studying its structure and center of mass motion. The wavepacket has a minimal size equal to the Compton wavelength, and has self-rotation about the average spin angular momentum, which gives rise to the spin magnetic moment. Geometric gauge structure in the center of mass motion provides a natural explanation of the spin-orbit coupling and various Yafet terms. Applications of the spin-Hall and spin-Nernst effects are discussed.     

Representation of the spin in the Dirac equation for the electron

The conventional interpretation of the spin matrices contained in the Dirac equation for the electron is considered to be mostly unintelligible in the operational sense. It is shown that it appears that the interpretation is often illogical. The necessity of a more comprehensible interpretation of the concerned equation is implied.     

Inconsistency of QED in the presence of Dirac monopoles

A precise formulation ofU (1) local gauge invariance in QED is presented, which clearly shows that the gauge coupling associated with the unphysical longitudinal photon field is non-observable and actually has an arbitrary value. We then re-examine the Dirac quantization condition and find that its derivation involves solely the unphysical longitudinal coupling. Hence an inconsistency inevitably arises in the presence of Dirac monopoles and this can be considered as a theoretical evidence against their existence. An alternative, independent proof of this conclusion is also presented.     

Dynamics of a Dirac particle in the theory with Lorentz invariance violation

Solutions to the Dirac equations have been obtained for particles interacting with vector, axial-vector, and tensor condensates within the framework of the Standard Model Extension. Possible applications of these solutions for describing the neutrino behavior in dense matter and electromagnetic field are considered.     

Dynamics of the magnetization in the heavy fermion system CeCu6

We have studied CeCu₆ by inelastic neutron scattering. We found both quasielastic and also inelastic transitions, which we interpret as residual crystal field transitions. The quasielastic linewidth is a strongly nonlinear function of temperature, with approximately _QE=5.0 meV at 300 K, with a crossover _QE=kT at about 13 K and with a residual value of _QE=(0)=0.50 meV forT=0 K. Below 5 K the quasielastic intensityI _QE decreases linearly with temperature. _stI _QE/T is in good agreement with direct measurements of the static susceptibility. The data are fully consistent with a nonordering groundstate of CeCu₆.     

Variational approach for the effects of periodic modulations on the spectrum of massless Dirac fermion

In the variational framework, we study the electronic energy spectrum of massless Dirac fermions of graphene subjected to one-dimensional oscillating magnetic and electrostatic fields centered around a constant uniform static magnetic field. We analyze the influence of the lateral periodic modulations in one direction, created by these oscillating electric and magnetic fields, on Dirac like Landau levels depending on amplitudes and periods of the field modulations. We compare our theoretical results with those found within the framework of non-degenerate perturbation theory. We found that the technique presented here yields energies lower than that obtained by the perturbation calculation, and thus gives more stable solutions for the electronic spectrum of massless Dirac fermion subjected to a magnetic field perpendicular to graphene layer under the influence of additional periodic potentials.