W.P.H. de Boer

Relativistic kinetic theory of quantum systems: III. Transport equation for a neutrino system

Abstract On the basis of the quantum-mechanical equations of motion and the statistical assumption that dynamical correlations present in the initial state may be ignored, a kinetic equation for a dilute neutrino system is derived. If the system is sufficiently uniform in space this equation reduces to the relativistic Boltzmann equation for massless particles with a quantum-mechanical transition probability.

Relativistic kinetic theory of quantum systems

For a dilute and nondegenerate relativistic spin-12 system two kinds of Wigner functions are defined: one has sixteen spinor components and the other four spin components. Their relationship is established. Statistical expressions for the current density, the energy-momentum density and the spin density are obtained in terms of both kinds of Wigner functions. The transformation properties of the latter under Lorentz transformations are discussed.

Relativistic kinetic theory of quantum systems: II. Neutrino-antineutrino system

Abstract It is shown that the macroscopic current density and energy-momentum density of a neutrino-antineutrino system may be expressed in terms of moments of two scalar Wigner functions, provided that the system is homogeneous on the scale of the de Broglie wavelength of the particles. The equilibrium form of these Wigner functions is established.

Relativistic transport equation for spin 12 particles

Abstract For the model of positive energy Dirac particles with short range interaction a transport equation for the one- particle Wigner function is obtained. This transport equation is a generalization of the non-relativistic Walsmann- Snider equation for spin particles.

A note on Keldysh's perturbation formalism

The expansion theorem of quantum field theoy relating Heisenberg operators to asymptotic free-field operators is rewritten by means of the time-path technique, originally due to Schwinger, which to date has only found application in statistical mechanics. The theorem is combined with Bogoliubovs initial condition of vanishing correlations in the infinite past to rederive Keldyshs perturbation scheme for non-equilibrium statistical Greens functions.

Transport properties of a neutrino-antineutrino mixture

The transport properties - heat conduction, diffusion, thermal diffusion and viscous flow - of a neutrino-antineutrino mixture are studied. It turns out that in a temperature field the more abundant component will diffuse against the temperature gradient.

On the derivation of quantum kinetic equations. I. Collision expansions

A straightforward scheme for deriving quantum kinetic equations is presented. It is based on Bogoliubovs initiai condition of vanishing correlations in the infinite past and consists in the elimination of an initial oneparticle Wigner function between two nonlinear functionals. By performing the elimination to second order in the density the quantum analog of the Choh-Uhlenbeck three-particle collision term is obtained. The scheme may be extended to include relativistic particles as well as particles with internal degrees of freedom.

The three-particle collision term in quantum kinetic theory

Abstract We outline a formalism for obtaining the three-particle collision term in quantum kinetic theory. The scheme is based on expansions in terms of initial distribution functions and Bogoliubovs initial condition of vanishing correlations in the infinite past.

Influence of the spin and the Weinberg-angle on the bulk viscosity of a neutrino-electron mixture

Abstract Results are presented for the first approximation to the bulk viscosity of a non-degenerate electron-neutrino system interacting in accordance with the Weinberg-Salam model. The influence of the electron spin and the Weinberg-angle are taken into account separately.

Separation processes in the primordial neutrino-antineutrino gas

The transport coefficients of a neutrino-antineutrino mixture are calculated on the basis of the neutral current weak interaction. From the values obtained it is concluded that matter and antimatter could separate in the universe during the primordial lepton era.