arXiv subjects
Publications and source records attributed to H. Arthur Weldon.
A nonperturbative proof is given that the chirally-invariant quark propagator contains both particle and hole singularities with different dispersion relations. Mesons made of a quark and a hole will produce dilepton pairs at masses characteristic of the plasma and with a distinct energy dependence.
The branch points of individual thermal self-energy diagrams at $k^{2}=4m^{2}, k^{2}=9m^{2},...$ are shown not to be branch points of the full thermal self-energy. Branch points of the full theory are determined by the complex, temperature-dependent energies of the quasiparticles, defined as the pole location, $k_{0}={\cal E}(\vec{k})$, of the exact retarded propagator. The full retarded self-energy is found to have branch points at $k_{0}=2{\cal E}(\vec{k}/2)$ and $k_{0}=3{\cal E}(\vec{k}/3)$ as well as cuts in the space-like region. The discontinuities across the branch cuts are complex. The advanced self-energy is related by reflection to the retarded.
By employing retarded and advanced propagators, Aurenche and Becherrawy showed how to rewrite the real-time thermal Feynman rules so that the temperature dependence is removed from the free propagators and transferred to the vertices. The present paper introduces retarded and advanced field operators and incorporates all temperature dependence into the interaction term of the Hamiltonian. Perturbative expansions of the Green functions in the Hamiltonian formulation give the correct results order by order in perturbation theory. The spectrum of the temperature-dependent Hamiltonian contains the thermal quasiparticles that produce poles in the propagators.
The thermal self-energy of gluons generally depends on four Lorentz-invariant functions. Only two of these occur in the hard thermal loop approximation of Braaten and Pisarski because of the abelian Ward identity $K_μΠ^{μν}_{\rm htl}=0$. However, for the exact self-energy $K_μΠ^{μν}\neq 0$. In linear gauges the Slavnov-Taylor identity is shown to require a non-linear relation among three of the Lorentz-invariant self-energy function: $(Π_{C})^{2}=(K^{2}-Π_{L})Π_{D}$. This reduces the exact gluon propagator to a simple form containing only two types of poles: one that determines the behavior of transverse electric and magnetic gluons and one that controls the longitudinally polarized electric gluons.
In momentum space the Feynman propagator $D_{F}(k)$ at non-zero temperature is defined by a simple dispersion relation with the familiar property of being an even function of $k^{0}$ and analytic for Re$(k^{0})^{2}>0$. The coordinate space form of the propagator $D_{F}(x)$ is expressed directly in terms of matrix elements of the field operator and requires a new type of operator ordering.
The radiation produced by a classical charged current coupled to a quantized $A_μ$ is first computed. To each order in $α$, all infrared divergences cancel between the virtual $γ$'s and the real $γ$'s that are absorbed from or emitted into the plasma. When all orders of perturbation theory are summed, the finite answer predicts a suppression of radiation with $ω< αT$. The analysis of QED then consists of two steps. First, a general probability at $T\neq 0$ is organized so that all the virtual $e^{\pm},γ$ are in the amplitudes and all the real $e^{\pm},γ$ are in the phase space integrations. Next, the cancellations of IR divergences between virtual and real are demonstrated.
As a preliminary step, the radiation produced by a classical charged current coupled to a quantized $A_μ$ is solved. To each order in $α$, all infrared divergences cancel between the virtual $γ$'s and the real $γ$'s absorbed from the plasma or emitted into the plasma. When all orders of perturbation theory are summed, the finite answer predicts a suppression of radiation with $ω< αT$. The analysis of QED then consists of two steps. First, a general probability at $T\neq 0$ is organized so that all the virtual $e^{\pm},γ$ are in the amplitudes and all the real $e^{\pm},γ$ are in the phase space integrations. Next, the cancellations of IR divergences between virtual and real are demonstrated.
The first-order bremsstrahlung emission spectrum is $αdω/ω$ at zero temperature. If the radiation is emitted into a region that contains a thermal distribution of photons, then the rate is increased by a factor $1+N(ω)$ where $N(ω)$ is the Bose-Einstein function. The stimulated emission changes the spectrum to $αTdω/ω^{2}$ for $ω\ll T$. If this were correct, an infinite amount of energy would be radiated in the low frequency modes. This unphysical result indicates a breakdown of perturbation theory. The paper computes the bremsstrahlung rate to all orders of perturbation theory, neglecting the recoil of the charged particle. When the perturbation series is summed, it has a different low-energy behavior. For $ω\llαT$, the spectrum is independent of $ω$ and has a value proportional to $dω/αT$ .