Gauge Independence and Relativistic Electron Dispersion Equation in Dense Media

We discuss the gauge parameter dependence of particle spectra in statistical quantum electrodynamics and conclude that the electron spectrum is gauge-parameter dependent. The physical spectrum being obtained in the Landau gauge, which leads to gauge invariance in a restricted class of gauge transformations.Comment: Style corrections 16 pages, three figures, RevTe

Effect of Fe3+ on Phase Relations in the Lower Mantle : Implications for Redox Melting in Stagnant Slabs

Recent studies have revealed that Earth's deep mantle may have a wider range of oxygen fugacities than previously thought. Such a large heterogeneity might be caused by material subducted into the deep mantle. However, high-pressure phase relations are poorly known in systems including Fe3+ at the top of the lower mantle, where the subducted slab may be stagnant. We therefore conducted high-pressure and high-temperature experiments using a multi-anvil apparatus to study the phase relations in a Fe3+-bearing system at 26 GPa and 1573–2073 K, at conditions prevailing at the top of the lower mantle. At temperatures below 1923 K, MgSiO3-rich bridgmanite, an Fe3+-rich oxide phase, and SiO2 coexist in the recovered sample. Quenched partial melt was observed above 1973 K, which is significantly lower than the solidus temperature of an equivalent Fe3+-free bulk composition. The partial melt obtained from the Fe3+-rich bulk composition has a higher iron content than coexisting bridgmanite, similar to the Fe2+-dominant system. The results suggest that strong mantle oxygen fugacity anomalies might alter the subsolidus and melting phase relations under lower mantle conditions. We conclude that (1) a small amount of melt may be generated from an Al-depleted region of a stagnant slab, such as subducted former banded-iron-formation, and (2) Fe3+ is not transported into the deep part of the lower mantle because of its incompatibility during melting

Two-loop Compton and annihilation processes in thermal QCD

We calculate the Compton and annihilation production of a soft static lepton pair in a quark-gluon plasma in the two-loop approximation. We work in the context of the effective perturbative expansion based on the resummation of hard thermal loops. Double counting is avoided by subtracting appropriate counterterms. It is found that the two-loop diagrams give contributions of the same order as the one-loop diagram. Furthermore, these contributions are necessary to obtain agreement with the naive perturbative expansion in the limit of vanishing thermal masses.Comment: Latex, 24 pages, postscript figures included with the package graphic

Non-Analytic Vertex Renormalization of a Bose Gas at Finite Temperature

We derive the flow equations for the symmetry unbroken phase of a dilute 3-dimensional Bose gas. We point out that the flow equation for the interaction contains parts which are non-analytic at the origin of the frequency-momentum space. We examine the way this non-analyticity affects the fixed point of the system of the flow equations and shifts the value of the critical exponent for the correlation length closer to the experimental result in comparison with previous work where the non-analyticity was neglected. Finally, we emphasize the purely thermal nature of this non-analytic behaviour comparing our approach to a previous work where non-analyticity was studied in the context of renormalization at zero temperature.Comment: 21 pages, 4 figure

Infrared Behavior of High-Temperature QCD

The damping rate \gamma_t(p) of on-shell transverse gluons with ultrasoft momentum p is calculated in the context of next-to-leading-order hard-thermal-loop-summed perturbation of high-temperature QCD. It is obtained in an expansion to second order in p. The first coefficient is recovered but that of order p^2 is found divergent in the infrared. Divergences from light-like momenta do also occur but are circumvented. Our result and method are critically discussed, particularly regarding a Ward identity obtained in the literature. When enforcing the equality between \gamma_t(0) and \gamma_l(0), a rough estimate of the magnetic mass is obtained. Carrying a similar calculation in the context of scalar quantum electrodynamics shows that the early ultrasoft-momentum expansion we make has little to do with the infrared sensitivity of the result.Comment: REVTEX4, 55 page

Collective fermionic excitations in systems with a large chemical potential

We study fermionic excitations in a cold ultrarelativistic plasma. We construct explicitly the quantum states associated with the two branches which develop in the excitation spectrum as the chemical potential is raised. The collective nature of the long wavelength excitations is clearly exhibited. Email contact: [email protected]: Saclay-T93/018 Email: [email protected]

SiO2 glass density to lower-mantle pressures

The convection or settling of matter in the deep Earth’s interior is mostly constrained by density variations between the different reservoirs. Knowledge of the density contrast between solid and molten silicates is thus of prime importance to understand and model the dynamic behavior of the past and present Earth. SiO2 is the main constituent of Earth’s mantle and is the reference model system for the behavior of silicate melts at high pressure. Here, we apply our recently developed x-ray absorption technique to the density of SiO2 glass up to 110 GPa, doubling the pressure range for such measurements. Our density data validate recent molecular dynamics simulations and are in good agreement with previous experimental studies conducted at lower pressure. Silica glass rapidly densifies up to 40 GPa, but the density trend then flattens to become asymptotic to the density of SiO2 minerals above 60 GPa. The density data present two discontinuities at ∼17 and ∼60  GPa that can be related to a silicon coordination increase from 4 to a mixed 5/6 coordination and from 5/6 to sixfold, respectively. SiO2 glass becomes denser than MgSiO3 glass at ∼40  GPa, and its density becomes identical to that of MgSiO3 glass above 80 GPa. Our results on SiO2 glass may suggest that a variation of SiO2 content in a basaltic or pyrolitic melt with pressure has at most a minor effect on the final melt density, and iron partitioning between the melts and residual solids is the predominant factor that controls melt buoyancy in the lowermost mantle

Solution to the 3-loop Φ\Phi-derivable Approximation for Scalar Thermodynamics

We solve the 3-loop $\Phi$-derivable approximation to the thermodynamics of the massless $\phi^4$ field theory by reducing it to a 1-parameter variational problem. The thermodynamic potential is expanded in powers of $g^2$ and $m/T$, where $g$ is the coupling constant, $m$ is a variational mass parameter, and $T$ is the temperature. There are ultraviolet divergences beginning at 6th order in $g$ that cannot be removed by renormalization. However the finite thermodynamic potential obtained by truncating after terms of 5th order in $g$ and $m/T$ defines a stable approximation to the thermodynamic functions.Comment: 4 pages, 1 figur

QED effective action at finite temperature

The QED effective Lagrangian in the presence of an arbitrary constant electromagnetic background field at finite temperature is derived in the imaginary-time formalism to one-loop order. The boundary conditions in imaginary time reduce the set of gauge transformations of the background field, which allows for a further gauge invariant and puts restrictions on the choice of gauge. The additional invariant enters the effective action by a topological mechanism and can be identified with a chemical potential; it is furthermore related to Debye screening. In concordance with the real-time formalism, we do not find a thermal correction to Schwinger's pair-production formula. The calculation is performed on a maximally Lorentz covariant and gauge invariant stage.Comment: 9 pages, REVTeX, 1 figure, typos corrected, references added, final version to appear in Phys. Rev.