Search results for "Dirac sea"
showing 6 items of 6 documents
Positron Production in Heavy Ion-Atom Collisions
1983
The question of pair creation in strong electrical fields is a very old problem. Already in 1929, within the framework of the new Dirac theory of the electron1, Klein considered the behaviour of an electron wave with a total energy E = ET + mec2 impinging on a one-dimensional step barrier potential Vo> mec2/e (fig. 1a). If the kinetic energy ET of an electron travelling on the z-axis from left to right is less than eVo, then for z>0 an exponentially damped wave function is expected as a solution of the Schrodinger equation. According to Klein’s calculations with the Dirac equation, this behaviour was also found for eVo-2mec2 <ET<eVo, but for a kinetic energy ET<eVo-2mec2 the wave function s…
Position space formulation for Dirac fermions on honeycomb lattice
2014
We study how to construct Dirac fermion defined on the honeycomb lattice in position space. Starting from the nearest neighbor interaction in tight binding model, we show that the Hamiltonian is constructed by kinetic term and second derivative term of three flavor Dirac fermions in which one flavor has a mass of cutoff order and the other flavors are massless. In this formulation the structure of the Dirac point is simplified so that its uniqueness can be easily shown even if we consider the next-nearest neighbor interaction. We also show the chiral symmetry at finite lattice spacing, which protects the masslessness of the Dirac fermion, and discuss the analogy with the staggered fermion f…
Neutrino-nucleon scattering rate in proto-neutron star matter
2002
We present a calculation of the neutrino-nucleon scattering cross-section which takes into account the nuclear correlations in the relativistic random phase approximation (RPA). Our approach is based on a quantum-hadrodynamics model with exchange of sigma, omega, pi, rho and delta mesons. In view of applications to neutrino transport in the final stages of supornova explosion and proto-neutron star cooling, we study the evolution of the neutrino mean free path as a function of density, proton-noutron asymmetry and temperature. Special attention was paid to the issues of renormalization of the Dirac sea, residual interactions in the tensor channel, coupling to the delta-meson and meson mixin…
Particles with Spin 1/2 and the Dirac Equation
2013
In order to identify the spin of a massive particle one must go to its rest system, perform rotations of the frame of reference, and study the transformation behaviour of one-particle states. This prescription was one of the essential results of Chap. 6. Furthermore, the spin \(1/2\) (electrons, protons, other fermions) is described by the fundamental representation of the group \(SU(2)\). The eigenstates of the observables \(\mathbf{{s}}^2\) and \(s_3\) transform by the \(D\)-matrix \(\mathbf{D }^{(1/2)}(\mathbf R )\) which is a two-valued function on \(\mathbb{R }^3\).
Radial coherent states for Dirac hydrogen-like atom
2002
In this paper we use an su(2) representation of the radial eigenfunction of the Dirac hydrogen-like atom and we build the Glauber coherent states and the displacement operator coherent states. We also calculate the average values of some observables corresponding to these states.
Dirac operator spectrum in the linear σ model
2003
Abstract The spectrum of the Dirac operator for the linear σ Model with quarks in the large Nc approximation is presented. The spectral density can be related to the chiral condensate which is obtained using renormalization group flow equations. For small eigenvalues, the Banks-Casher relation and the vanishing linear correaction are recovered. The spectrum beyond the low energy regime is discussed.