Damping Rate of Quasiparticles in Degenerate Ultrarelativistic Plasmas

We compute the damping rate of a fermion in a dense relativistic plasma at zero temperature. Just above the Fermi sea, the damping rate is dominated by the exchange of soft magnetic photons (or gluons in QCD) and is proportional to $(E-\mu)$, where E is the fermion energy and $\mu$ the chemical potential. We also compute the contribution of soft electric photons and of hard photons. As in the nonrelativistic case, the contribution of longitudinal photons is proportional to $(E-\mu)^2$, and is thus non leading in the relativistic case.Comment: 8 pages, RevTex, 1 figur

Fermionic dispersion relations in ultradegenerate relativistic plasmas beyond leading logarithmic order

We determine the dispersion relations of fermionic quasiparticles in ultradegenerate plasmas by a complete evaluation of the on-shell hard-dense-loop-resummed one-loop fermion self energy for momenta of the order of the Fermi momentum and above. In the case of zero temperature, we calculate the nonanalytic terms in the vicinity of the Fermi surface beyond the known logarithmic approximation, which turn out to involve fractional higher powers in the energy variable. For nonzero temperature (but much smaller than the chemical potential), we obtain the analogous expansion in closed form, which is then analytic but involves polylogarithms. These expansions are compared with a full numerical evaluation of the resulting group velocities and damping coefficients.Comment: 9 pages, 2 figures, REVTeX4, v2: minor improvement

Charged-Particle Decay at Finite Temperature

Radiative corrections to the decay rate of charged fermions caused by the presence of a thermal bath of photons are calculated in the limit when temperatures are below the masses of all charged particles involved. The cancellation of finite-temperature infrared divergences in the decay rate is described in detail. Temperature-dependent radiative corrections to a two-body decay of a hypothetical charged fermion and to electroweak decays of a muon are given. We touch upon possible implications of these results for charged particles in the early Universe.Comment: 18 pages, 6 figures. v2: typos corrected, bibliography revised, content matches published versio

Weinberg power counting and the quark determinant at small chemical potential

We construct an effective action for QCD by expanding the quark determinant in powers of the chemical potential at finite temperature in the case of massless quarks. To cut the infinite series we adopt the Weinberg power counting criteria. We compute the minimal effective action (~p^4), expanding in the external momentum, which implies the use of the hard thermal loop approximation. Our main result is a gauge invariant expression for the phase theta of the functional determinant in QCD, and recovers dimensional reduction in the high-temperature limit. We compute, analytically, in the range of p << 2 pi T, including perturbative and nonperturbative contributions, the latter treated within the mean field approximation. Implications for lattice simulations are briefly discussed.Comment: 5 pages, 2 figures. v2: title changed, expanded discussion and added example (calculation of at high temperature). Published in PR

Gamma flashes from relativistic electron-positron plasma droplets

Ultra-intense lasers are expected to produce, in near future, relativistic electron-positron plasma droplets. Considering the local photon production rate in complete leading order in quantum electrodynamics (QED), we point out that these droplets are interesting sources of gamma ray flashesComment: 4 pages, 6 figures; Text has been revised and new refs. are adde

Momentum Broadening of a Fast Parton in a Perturbative Quark-Gluon Plasma

The average transverse momentum transfer per unit path length to a fast parton scattering elastically in a perturbative quark-gluon plasma is related to the radiative energy loss of the parton. We first calculate the momentum transfer coefficient $\hat q$ in terms of a classical Langevin problem and then define it quantum-mechanically through scattering matrix element. After treating the well known case of a quark-gluon plasma in equilibrium we consider an off-equilibrium unstable plasma. As a specific example, we treat the two-stream plasma with unstable modes of longitudinal chromoelectric field. In the presence of the instabilities, $\hat q$ is shown to exponentially grow in time.Comment: Updated version containing an analysis of insufficiencies in previous calculations of momentum broadening in unstable plasma

The effect of an imaginary part of the Schwinger-Dyson equation at finite temperature and density

We examined the effect of an imaginary part of the ladder approximation Schwinger-Dyson equation. We show the imaginary part enhances the effect of the first order transition, and affects a tricritical point. In particular, a chemical potential at a tricritical point is moved about 200(MeV). Thus, one should not ignore the imaginary part. On the other hand, since an imaginary part is small away from a tricritical point, one should be able to ignore an imaginary part. In addition, we also examined the contribution of the wave function renormalization constant.Comment: 12 pages, 14 figure

A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density

We adapt the Goldstone theorem to study spontaneous symmetry breaking in relativistic theo- ries at finite charge density. It is customary to treat systems at finite density via non-relativistic Hamiltonians. Here we highlight the importance of the underlying relativistic dynamics. This leads to seemingly new results whenever the charge in question is spontaneously broken and does not commute with other broken charges. We find that that the latter interpolate gapped excitations. In contrast, all existing versions of the Goldstone theorem predict the existence of gapless modes. We derive exact non-perturbative expressions for their gaps, in terms of the chemical potential and of the symmetry algebra.Comment: 5 pages. v2: minor modifications, matches the PRL versio

Hard thermal effective action in QCD through the thermal operator

Through the application of the thermal operator to the zero temperature retarded Green's functions, we derive in a simple way the well known hard thermal effective action in QCD. By relating these functions to forward scattering amplitudes for on-shell particles, this derivation also clarifies the origin of important properties of the hard thermal effective action, such as the manifest Lorentz and gauge invariance of its integrand.Comment: 6 pages, contribution of the quarks to the effective action included and one reference added, version to be published in Phys. Rev.

Next-to-leading order static gluon self-energy for anisotropic plasmas

In this paper the structure of the next-to-leading (NLO) static gluon self energy for an anisotropic plasma is investigated in the limit of a small momentum space anisotropy. Using the Ward identities for the static hard-loop (HL) gluon polarization tensor and the (nontrivial) static HL vertices, we derive a comparatively compact form for the complete NLO correction to the structure function containing the space-like pole associated with magnetic instabilities. On the basis of a calculation without HL vertices, it has been conjectured that the imaginary part of this structure function is nonzero, rendering the space-like poles integrable. We show that there are both positive and negative contributions when HL vertices are included, highlighting the necessity of a complete numerical evaluation, for which the present work provides the basis.Comment: 9 pages, 2 figure