Pair creation in a uniform classical electromagnetic field (Schwinger mechanism) is studied focusing on the time evolution of the distribution of created particles. The time evolution of the distribution in time-dependent fields is also presented as well as effects of back reaction. Motivated by the Glasma flux tube, which may be formed at the initial stage of heavy-ion collisions, we investigate effects of a magnetic field parallel to an electric field, and find that the magnetic field makes the evolution of a fermion system faster.Comment: 57pages, 44figures. v2: typos corrected, references added, to appear in Ann.Phy

In this article, we review recent theoretical works on the Schwinger mechanism of particle production in external electrical fields. Although the non-perturbative Schwinger mechanism is at the center of this discussion, many of the approaches that we discuss can cope with general time and space dependent fields, and therefore also capture the perturbative contributions to particle production.

Recent classical-statistical numerical simulations have established the "bottom-up" thermalization scenario of Baier et al. [1] as the correct weak coupling effective theory for thermalization in ultrarelativistic heavy-ion collisions. We perform a parametric study of photon production in the various stages of this bottom-up framework to ascertain the relative contribution of the off-equilibrium "Glasma" relative to that of a thermalized Quark-Gluon Plasma. Taking into account the constraints imposed by the measured charged hadron multiplicities at RHIC and the LHC, we find that Glasma contributions are important especially for large values of the saturation scale at both energies. These non-equilibrium effects should therefore be taken into account in studies where weak coupling methods are employed to compute photon yields.

The time evolution of a system where a uniform and classical SU(3) color electric field and quantum fields of quarks are dynamically coupled with each other is studied focusing on nonperturbative pair creation and its back reaction. We characterize the color direction of the electric field in a gauge invariant way, and investigate its dependence. Momentum distributions of created quarks show plasma oscillation as well as quantum effects such as the Pauli blocking and interference. Pressure of the system is also calculated, and we show that pair creation moderates degree of anisotropy of pressure. Furthermore, enhancement of pair creation and induction of chiral charge under a color magnetic field which is parallel to the electric field are discussed.

We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.Comment: 37 pages, 21 figure

In this paper, we show how classical statistical field theory techniques can be used to efficiently perform the numerical evaluation of the nonperturbative Schwinger mechanism of particle production by quantum tunneling. In some approximation, we also consider the back-reaction of the produced particles on the external field, as well as the self-interactions of the produced particles.1 This observable should not be confused with the probability P 1 of producing exactly one particle-antiparticle pair, that would be obtained from the matrix element 0out φ(x) 0 in . The average number of produced particles (i.e. the integral over p of dN 1 /d 3 p) is related to the probabilities Pn by N 1 = n nPn. N 1 is usually easier to calculate than the individual Pn, thanks to simplifications related to the completeness of the set of possible final states.2 The contribution of the lower boundary is in fact 0 in a † in (p)a in (p) 0 in = 0. 3 At this stage, the object φ is still an operator, and one should keep in mind that the commutator [φ, φ] is not zero.

We report on a numerical study of the Boltzmann equation including 2 ↔ 2 scatterings of gluons and quarks in an overoccupied Glasma undergoing longitudinal expansion. We find that when a cascade of gluon number to the infrared occurs, corresponding to an infrared enhancement analogous to a transient Bose-Einstein condensate, gluon distributions qualitatively reproduce the results of classical-statistical simulations for the expanding Glasma.These include key features of the distributions that are not anticipated in the "bottom-up" thermalization scenario. We also find that quark distributions, like those of gluons, satisfy self-similar scaling distributions in the overoccupied Glasma. We discuss the implications of these results for a deeper understanding of the self-similarity and universality of parton distributions in the Glasma.

We discuss gluon production by the Schwinger mechanism in collinear colorelectric and magnetic fields which may be realized in pre-equilibrium stages of ultrarelativistic heavy-ion collisions. Fluctuations of non-Abelian gauge fields around a purely color-magnetic field contain exponentially growing unstable modes in a longitudinally soft momentum region, which is known as the Nielsen-Olesen instability. With a color-electric field imposed parallelly to the color-magnetic field, we can formulate this instability as the Schwinger mechanism. This is because soft unstable modes are accelerated by the electric fields to escape from the instability condition. Effects of instability remain in the transverse spectrum of particle modes, leading to an anomalously intense Schwinger particle production.