Classical Simulation of Quantum Fields II

We consider the classical time evolution of a real scalar field in 2 dimensional Minkowski space with a $\lambda \phi^4$ interaction. We compute the spatial and temporal two-point correlation functions and extract the renormalized mass of the interacting theory. We find our results are consistent with the one- and two-loop quantum computation. We also perform Monte Carlo simulations of the quantum theory and conclude that the classical scheme is able to produce more accurate results with a fraction of the CPU time.Comment: 16 pages, 8 figures, now matches published versio

Evolution of cosmic superstring networks: a numerical simulation

We study the formation and evolution of an interconnected string network in large-scale field-theory numerical simulations, both in flat spacetime and in expanding universe. The network consists of gauge U(1) strings of two different kinds and their bound states, arising due to an attractive interaction potential. We find that the network shows no tendency to ``freeze'' and appears to approach a scaling regime, with all characteristic lengths growing linearly with time. Bound strings constitute only a small fraction of the total string length in the network.Comment: 16 pages, 13 figures; Minor changes; Matches published versio

Real-time nonequilibrium dynamics in hot QED plasmas: dynamical renormalization group approach

We study the real-time nonequilibrium dynamics in hot QED plasmas implementing a dynamical renormalization group and using the hard thermal loop (HTL) approximation. The focus is on the study of the relaxation of gauge and fermionic mean fields and on the quantum kinetics of the photon and fermion distribution functions. For semihard photons of momentum eT << k << T we find to leading order in the HTL that the gauge mean field relaxes in time with a power law as a result of infrared enhancement of the spectral density near the Landau damping threshold. The dynamical renormalization group reveals the emergence of detailed balance for microscopic time scales larger than 1/k while the rates are still varying with time. The quantum kinetic equation for the photon distribution function allows us to study photon production from a thermalized quark-gluon plasma (QGP) by off-shell effects. We find that for a QGP at temperature T ~ 200 MeV and of lifetime 10 < t < 50 fm/c the hard (k ~ T) photon production from off-shell bremsstrahlung (q -> q \gamma and \bar{q} -> \bar{q}\gamma) at O(\alpha) grows logarithmically in time and is comparable to that produced from on-shell Compton scattering and pair annihilation at O(\alpha \alpha_s). Fermion mean fields relax as e^{-\alpha T t ln(\omega_P t)} with \omega_P=eT/3 the plasma frequency, as a consequence of the emission and absorption of soft magnetic photons. A quantum kinetic equation for hard fermions is obtained directly in real time from a field theoretical approach improved by the dynamical renormalization group. The collision kernel is time-dependent and infrared finite.Comment: RevTeX, 46 pages, including 5 EPS figures, published versio

Dynamical Renormalization Group Approach to Quantum Kinetics in Scalar and Gauge Theories

We derive quantum kinetic equations from a quantum field theory implementing a diagrammatic perturbative expansion improved by a resummation via the dynamical renormalization group. The method begins by obtaining the equation of motion of the distribution function in perturbation theory. The solution of this equation of motion reveals secular terms that grow in time, the dynamical renormalization group resums these secular terms in real time and leads directly to the quantum kinetic equation. We used this method to study the relaxation in a cool gas of pions and sigma mesons in the O(4) chiral linear sigma model. We obtain in relaxation time approximation the pion and sigma meson relaxation rates. We also find that in large momentum limit emission and absorption of massless pions result in threshold infrared divergence in sigma meson relaxation rate and lead to a crossover behavior in relaxation. We then study the relaxation of charged quasiparticles in scalar electrodynamics (SQED). While longitudinal, Debye screened photons lead to purely exponential relaxation, transverse photons, only dynamically screened by Landau damping lead to anomalous relaxation, thus leading to a crossover between two different relaxational regimes. We emphasize that infrared divergent damping rates are indicative of non-exponential relaxation and the dynamical renormalization group reveals the correct relaxation directly in real time. Finally we also show that this method provides a natural framework to interpret and resolve the issue of pinch singularities out of equilibrium and establish a direct correspondence between pinch singularities and secular terms. We argue that this method is particularly well suited to study quantum kinetics and transport in gauge theories.Comment: RevTeX, 40 pages, 4 eps figures, published versio