Dynamical Renormalization Group Approach to Quantum Kinetics in Scalar and Gauge Theories
arXiv:hep-ph/9909369 · doi:10.1103/PhysRevD.61.065006
Abstract
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.
RevTeX, 40 pages, 4 eps figures, published version
References in corpus (60)
- The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory
- Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory
- Resummation in a Hot Scalar Field Theory
- Dissipation via Particle Production in Scalar Field Theories
- From Quantum Field Theory to Hydrodynamics: Transport Coefficients and Effective Kinetic Theory
- The Search for the Quark-Gluon Plasma
- pQCD-based Approach to Parton Production and Equilibration in High-Energy Nuclear Collisions
- Non-perturbative computation of gluon mini-jet production in nuclear collisions at very high energies
- Effective dynamics of soft non-abelian gauge fields at finite temperature
- Renormalization Group Theory for Global Asymptotic Analysis
- Analytic and Numerical Study of Preheating Dynamics
- Reheating and Thermalization, Linear Vs. Non-Linear Relaxation
- Optimized Perturbation Theory at Finite Temperature
- Phase transitions in quantum chromodynamics
- Hot B violation, color conductivity, and log(1/alpha) effects
- A Precursor of Chiral Symmetry Restoration in the Nuclear Medium
- A Geometrical Formulation of the Renormalization Group Method for Global Analysis
- Damping rates for moving particles in hot QCD
- From Reversible Quantum Microdynamics to Irreversible Quantum Transport
- Propagation of Cool Pions
- A Boltzmann Equation for the QCD Plasma
- Lifetimes of quasiparticles and collective excitations in hot QED plasmas
- Lifetime of quasiparticles in hot QED plasmas
- Chiral symmetry at finite temperature: linear vs nonlinear -models
- Screening of initial parton production in ultrarelativistic heavy-ion collisions
- Real-Time Dynamics with Fermions on a Lattice
- Dynamical renormalization group resummation of finite temperature infrared divergences
- Resummations in Hot Scalar Electrodynamics
- The Renormalization-Group Method Applied to Asymptotic Analysis of Vector Fields
- Forming Disoriented Chiral Condensates through Fluctuations
- Relaxation and Kinetics in Scalar Field Theories
- The Bloch-Nordsieck propagator at finite temperature
- Problems of Perturbation Series in Non-Equilibrium Quantum Field Theories
- Particle Production and Effective Thermalization in Inhomogeneous Mean Field Theory
- Hydrodynamics of nuclear collisions with initial conditions from perturbative QCD
- Real-time Relaxation and Kinetics in Hot Scalar QED: Landau Damping
- Evolution of Inhomogeneous Condensates after Phase Transitions
- Quantum Field Kinetics of QCD: Quark-Gluon Transport Theory for Lightcone Dominated Processes
- Thermalization and pinch singularities in non-equilibrium quantum field theory
- The gauge invariant effective potential: equilibrium and non-equilibrium aspects
- Interpretation and resolution of pinch singularities in non-equilibrium quantum field theory
- Anomalous Kinetics of Hard Charged Particles: Dynamical Renormalization Group Resummation
- Fermion Damping in a Fermion-Scalar Plasma
- Non-equilibrium QCD: Interplay of hard and soft dynamics in high-energy multi-gluon beams
- Out of Equilibrium Quantum Field Theory --- Perturbation Theory and Generalized Boltzmann Equation
- Formation and Evolution of Quark-Gluon Plasma at RHIC and LHC
- Nonequilibrium perturbation theory for complex scalar fields
- Two mechanisms for the elimination of pinch singularities in out of equilibrium thermal field theories
- Simulating hot Abelian gauge dynamics
- Renormalization-group Resummation of a Divergent Series of the Perturbative Wave Functions of Quantum Systems
- Order parameter evolution in scalar QFT: renormalization group resummation of secular terms
- Thermal Two Point Function of a Heavy Muon in hot QED plasma within Bloch Nordsieck Approximation
- Pre-thermalization dynamics: initial conditions for QGP at the LHC and RHIC from perturbative QCD
- Real Time Dynamics of Colliding Gauge Fields and the ''Glue Burst''
- Topics in the Transport Theory of Quark-Gluon Plasma
- Damping Rate of a Scalar Particle in Hot Scalar QED
- Effective theory for the soft fluctuation modes in the spontaneously broken phase of the N-component scalar field theory
- Renormalization of number density in nonequilibrium quantum-field theory and absence of pinch singularities
- Finite temperature effective action and thermalization of perturbations
- The Boltzmann Equation in Scalar Field Theory
Cited by in corpus (49)
- Advances in perturbative thermal field theory
- Dark matter clustering: a simple renormalization group approach
- Dynamical renormalization group approach to relaxation in quantum field theory
- The Fate of the Alpha-Vacuum
- Hydrodynamic transport functions from quantum kinetic theory
- Condensates and quasiparticles in inflationary cosmology: mass generation and decay widths
- The Boltzmann Equation from Quantum Field Theory
- Particle abundance in a thermal plasma: quantum kinetics vs. Boltzmann equation
- Non-Fermi Liquid Aspects of Cold and Dense QED and QCD: Equilibrium and Non-Equilibrium
- Magnetic field generation from non-equilibrium phase transitions
- Taming the alpha-vacuum
- Real-time nonequilibrium dynamics in hot QED plasmas: dynamical renormalization group approach
- Large scale magnetogenesis from a non-equilibrium phase transition in the radiation dominated era
- Finite Width in out-of-Equilibrium Propagators and Kinetic Theory
- Baryon Asymmetry of the Universe without Boltzmann or Kadanoff-Baym
- Minding one's P's and Q's : from the one loop effective action in quantum field theory to classical transport theory
- Enhanced photon production from quark-gluon plasma: Finite-lifetime effect
- Renormalization Group Method Applied to Kinetic Equations: roles of initial values and time
- Dynamical renormalization group approach to transport in ultrarelativistic plasmas: the electrical conductivity in high temperature QED
- On the Langevin description of nonequilibrium quantum fields
- Transport Theory beyond Binary Collisions
- Dynamical renormalization group approach to the Altarelli-Parisi-Lipatov equations
- Are direct photons a clean signal of a thermalized quark gluon plasma?
- Enhanced thermal production of hard dileptons by processes
- Relativistic Causal Hydrodynamics Derived from Boltzmann Equation: a novel reduction theoretical approach
- Renormalization group and nonequilibrium action in stochastic field theory
- Renormalization Group Approach to Cosmological Back Reaction Problems
- Non-equilibrium quantum plasmas in scalar QED: photon production, magnetic and Debye masses, and conductivity
- Direct photons: a nonequilibrium signal of the expanding quark-gluon plasma
- Derivation of second-order relativistic hydrodynamics for reactive multi-component systems
- Quantum renormalization group
- A simple out-of-equilibrium field theory formalism ?
- Out of Equilibrium Thermal Field Theories - Finite Time after Switching on the Interaction - Wigner Transforms of Projected Functions
- Oscillations and evolution of a hot and dense gas of flavor neutrinos: a quantum field theory study
- Photon production from a thermalized quark gluon plasma: quantum kinetics and nonperturbative aspects
- Time evolution in linear response: Boltzmann equations and beyond
- The effect of memory on relaxation in a scalar field theory
- Spectral function of the Bloch-Nordsieck model at finite temperature
- Infrared dressing in real time: emergence of anomalous dimensions
- Generalized Boltzmann equations for on-shell particle production in a hot plasma
- Non-Equilibrium Large N Yukawa Dynamics: marching through the Landau pole
- Direct Photons from Hot Quark Matter in Renormalized Finite-Time-Path QED
- Thermalization by off-shell processes: the virtues of small virtuality
- The electron thermal propagator at p>>T: An entire function of p_{0}
- Threshold and infrared singularities: time evolution, asymptotic state and entanglement entropy
- Purely perturbative Boltzmann equation for hot non-Abelian gauge theories
- Non-Markovian source term for particle production by a self-interacting scalar field in the large-N approximation
- Nonequilibrium Phenomena in Quantum Field Theory: From Linear Response to Dynamical Renormalization Group
- Nonperturbative evaluation of quantum particle production in parametric resonance enhanced by noise