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Register a new userRelativistic Quantum Transport Theory for Electrodynamics
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We investigate the relationship between the covariant and the three-dimensional (equal-time) formulations of quantum kinetic theory. We show that the three-dimensional approach can be obtained as the energy average of the covariant formulation. We illustrate this statement in scalar and spinor QED. For scalar QED we derive Lorentz covariant transport and constraint equations directly from the Klein-Gordon equation rather than through the previously used Feshbach-Villars representation. We then consider pair production in a spatially homogeneous but time-dependent electric field and show that the pair density is derived much more easily via the energy averaging method than in the equal-time representation. Proceeding to spinor QED, we derive the covariant version of the equal-time equation derived by Bialynicki-Birula et al. We show that it must be supplemented by another self-adjoint equation to obtain a complete description of the covariant spinor Wigner operator. After spinor decomposition and energy average we study the classical limit of the resulting three-dimensional kinetic equations. There are only two independent spinor components in this limit, the mass density and the spin density, and we derive also their covariant equations of motion. We then show that the equal-time kinetic equation provides a complete description only for constant external electromagnetic fields, but is in general incomplete. It must be supplemented by additional constraints which we derive explicitly from the covariant formulation.
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A relativistic density-functional theory based on a Fock-space effective quantum-electrodynamics (QED) Hamiltonian using the Coulomb or Coulomb-Breit two-particle interaction is developed. This effective QED theory properly includes the effects of vacuum polarization through the creation of electron-positron pairs but does not include explicitly the photon degrees of freedom. It is thus a more tractable alternative to full QED for atomic and molecular calculations. Using the constrained-search formalism, a Kohn-Sham scheme is formulated in a quite similar way to non-relativistic density-functional theory, and some exact properties of the involved density functionals are studied, namely charge-conjugation symmetry and uniform coordinate scaling. The usual no-pair Kohn-Sham scheme is obtained as a well-defined approximation to this relativistic density-functional theory.
In this paper, we compare the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We obtain an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. We find: (1) Potential $V_{RMF}$ of the RMF theory for nucleons has the wave functions $f$ and $g$ with joint part $h$ coincident exactly with the nucleon wave function of DOS model with potential $V_{rm shell}$. But, a difference between $V_{RMF}$ and $V_{rm shell}$ is essential for any nucleus. (2) The nucleon wave functions and densities obtained by the DOS and RMF theories are essentially different. The nucleon densities of the RMF theory contradict to knowledge about distribution of the proton and neutron densities inside the nuclei obtained from experimental data. This indicates that $g$ and $f$ have no sense of the wave functions of quantum physics. But, $h$ provides proper description of quantum properties of nucleons inside the nucleus. (3) We calculate meson function $w^{0}$ and potential $V_{w}$ in RMF theory based on the found nucleon density. (4) $f$ and $g$ are not solutions of Dirac equation with $V_{w}$. If the meson theory describes quantum properties of nucleus well, then a difference between $V_{w}$ and $V_{RMF}$ should be as small as possible. We introduce new quantum corrections characterizing difference between these potentials. We find that (a) The function $w^{0}$ should be reinforced strongly, (b) The corrections are necessary to describe the quantum properties of the nuclei.
We derive a quantum kinetic theory for QED including both elastic and inelastic collisions with screening effect. By assuming parity invariance at the lowest order in $hbar$, we find the classical limit of the kinetic theory generalizes the well-known classical kinetic theory to massive case. The resulting classical kinetic theory simplifies when fermion bare mass is much greater than thermal mass. In this case only elastic collision is relevant and screening is only needed for Coulomb scattering. For a given solution to the classical kinetic theory, we find at $O(hbar)$ non-dynamical part of the quantum correction to Wigner functions for fermion and photon, which gives rise to spin polarization for fermion and photon respectively. Other contributions to spin polarizations from dynamical part of the correction to Wigner function are possible when parity violating sources are present.
Within the relativistic quantum field theory, we analyze the differences between the $pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.
Relativistic quantum molecular dynamics based on the relativistic mean field theory (RQMD.RMF) is extended by including momentum-dependent potential. The equation of state (EoS) dependence of the directed and the elliptic flow of protons in the beam energy range of $2.3 < sqrt{s_{NN}}< 20$ GeV is examined. It is found that the directed flow depends strongly on the optical potential at high energies,$sqrt{s_{NN}} > 3 $ GeV, where no information is available experimentally. The correlation between effective mass at saturation density and the optical potential is found: smaller values of effective mass require smaller strengths of the optical potential to describe the directed flow data.This correlation can also be seen in the beam energy dependence of the elliptic flow at $sqrt{s_{NN}}>3$ GeV, although its effect is rather weak. On the other hand, stiff EoS is required to describe the elliptic flow at lower energies.Experimental constraints on the optical potential from $pA$ collisions will provide important information on the EoS at high energies.The proton directed and the elliptic flow are well described in the RQMD.RMF model from $sqrt{s_{NN}}=2.3$ to 8.8 GeV. In contrast,to reproduce the collapse of the directed flow above 10 GeV, pressure has to be reduced, which indicates a softening of the EoS around $sqrt{s_{NN}} =10 $ GeV.
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