Pair production in a strong electric field: an initial value problem in quantum field theory

We review recent achievements in the solution of the initial-value problem for quantum back-reaction in scalar and spinor QED. The problem is formulated and solved in the semiclassical mean-field approximation for a homogeneous, time-dependent electric field. Our primary motivation in examining back-reaction has to do with applications to theoretical models of production of the quark-gluon plasma, though we here address practicable solutions for back-reaction in general. We review the application of the method of adiabatic regularization to the Klein-Gordon and Dirac fields in order to renormalize the expectation value of the current and derive a finite coupled set of ordinary differential equations for the time evolution of the system. Three time scales are involved in the problem and therefore caution is needed to achieve numerical stability for this system. Several physical features, like plasma oscillations and plateaus in the current, appear in the solution. From the plateau of the electric current one can estimate the number of pairs before the onset of plasma oscillations, while the plasma oscillations themselves yield the number of particles from the plasma frequency. We compare the field-theory solution to a simple model based on a relativistic Boltzmann-Vlasov equation, with a particle production source term inferred from the Schwinger particle creation rate and a Pauli-blocking (or Bose-enhancement) factor. This model reproduces very well the time behavior of the electric field and the creation rate of charged pairs of the semiclassical calculation. It therefore provides a simple intuitive understanding of the nature of the solution since nearly all the physical features can be expressed in terms of the classical distribution function.Comment: Old paper, already published, but in an obscure journa

Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum

We show that the gluon distribution function for very large nuclei may be computed for small transverse momentum as correlation functions of an ultraviolet finite two dimensional Euclidean field theory. This computation is valid to all orders in the density of partons per unit area, but to lowest order in $\alpha_s$. The gluon distribution function is proportional to $1/x$, and the effect of the finite density of partons is to modify the dependence on transverse momentum for small transverse momentum.Comment: TPI--MINN--93--52/T, NUC--MINN--93--28/T, UMN--TH--1224/93, LaTex, 11 page

Back-reaction in a cylinder

A system is studied in which initially a strong classical electric field exists within an infinitely-long cylinder and no charges are present. Subsequently, within the cylinder, pairs of charged particles tunnel out from the vacuum and the current produced through their acceleration by the field acts back on the field, setting up plasma oscillations. This yields a rough model of phenomena that may occur in the pre-equilibrium formation phase of a quark-gluon plasma. In an infinite volume, this back-reaction has been studied in a field-theory description, and it has been found that the results of a full calculation of this sort are well represented in a much simpler transport formalism. It is the purpose here to explore that comparison for a situation involving a cylindrical volume of given radius.Comment: 19 pages plus 13 figure

Relativistic Kinetic Equations for Electromagnetic, Scalar and Pseudoscalar Interactions

We derive the kinetic equations for both the covariant and equal-time Wigner functions of Dirac particles with electromagnetic, scalar and pseudoscalar interactions. We emphasize the constraint equations for the spinor components in the equal-time formulation.Comment: 12 pages, no figures, revte

Pair creation: back-reactions and damping

We solve the quantum Vlasov equation for fermions and bosons, incorporating spontaneous pair creation in the presence of back-reactions and collisions. Pair creation is initiated by an external impulse field and the source term is non-Markovian. A simultaneous solution of Maxwell's equation in the presence of feedback yields an internal current and electric field that exhibit plasma oscillations with a period tau_pl. Allowing for collisions, these oscillations are damped on a time-scale, tau_r, determined by the collision frequency. Plasma oscillations cannot affect the early stages of the formation of a quark-gluon plasma unless tau_r >> tau_pl and tau_pl approx. 1/Lambda_QCD approx 1 fm/c.Comment: 16 pages, 6 figure, REVTEX, epsfig.st

Dileptons from Disoriented Chiral Condensates

Disoriented chiral condensates or long wavelength pionic oscillations and their interaction with the thermal environment can be a significant source of dileptons. We calculate the yield of such dilepton production within the linear sigma model, both in a quantal mean-field treatment and in a semi-classical approximation. We then illustrate the basic features of the dilepton spectrum in a schematic model. We find that dilepton yield with invariant mass near and below $2m_{\pi}$ due to the soft pion modes can be up to two orders of magnitude larger than the corresponding equilibrium yield.Comment: 22 pages, 8 figures, uses epsf-styl

Schwinger Mechanism for Gluon Pair Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field

We study Schwinger mechanism for gluon pair production in the presence of arbitrary time-dependent chromo-electric background field $E^a(t)$ with arbitrary color index $a$=1,2,...8 in SU(3) by directly evaluating the path integral. We obtain an exact expression for the probability of non-perturbative gluon pair production per unit time per unit volume and per unit transverse momentum $\frac{dW}{d^4x d^2p_T}$ from arbitrary $E^a(t)$. We show that the tadpole (or single gluon) effective action does not contribute to the non-perturbative gluon pair production rate $\frac{dW}{d^4x d^2p_T}$. We find that the exact result for non-perturbative gluon pair production is independent of all the time derivatives $\frac{d^nE^a(t)}{dt^n}$ where $n=1,2,....\infty$ and has the same functional dependence on two casimir invariants $[E^a(t)E^a(t)]$ and $[d_{abc}E^a(t)E^b(t)E^c(t)]^2$ as the constant chromo-electric field $E^a$ result with the replacement: $E^a \to E^a(t)$. This result may be relevant to study the production of a non-perturbative quark-gluon plasma at RHIC and LHC.Comment: 13 pages latex, Published in European Physical Journal