Nonequilibrium Phenomena in Quantum Field Theory: From Linear Response to Dynamical Renormalization Group
This thesis is devoted to studying aspects of real-time nonequilibrium dynamics in quantum field theory by implementing an initial value formulation of quantum field theory. The main focus is on the linear relaxation of mean fields and quantum kinetics in nonequilibrium multiparticle quantum systems with potential applications to ultrarelativistic heavy ion collisions, cosmological phase transitions and condensed matter systems. We first study the damping of fermion mean fields in a fermion-scalar plasma with a view towards understanding baryon transport phenomena during electroweak baryogenesis. Secondly, we apply and extend the renormalization group method to study nonequilibrium dynamics with the goals of constructing a quantum kinetic description that goes beyond usual Boltzmann kinetics and understanding anomalous relaxation associated with infrared phenomena. The final part of this thesis presents a real-time kinetic analysis of direct photon production from a quark-gluon plasma created in ultrarelativistic heavy ion collisions. We show that the direct photon yield is significantly enhanced by the lowest order energy-nonconserving processes originated in the transient lifetime of the quark-gluon plasma.

title: Dynamical electron mass in a strong magnetic field
abstract: Motivated by recent interest in understanding properties of strongly magnetized matter, we study the dynamical electron mass generated through approximate chiral symmetry breaking in QED in a strong magnetic field. We reliably calculate the dynamical electron mass by numerically solving the nonperturbative Schwinger-Dyson equations in a consistent truncation within the lowest Landau level approximation. It is shown that the generation of dynamical electron mass in a strong magnetic field is significantly enhanced by the perturbative electron mass that explicitly breaks chiral symmetry in the absence of a magnetic field.

title: Nonequilibrium relaxation of Bose-Einstein condensates: Real-time equations of motion and Ward identities
abstract: We present a field-theoretical method to obtain consistently the equations of motion for small amplitude condensate perturbations in a homogeneous Bose-condensed gas directly in real time. It is based on a linear response and combines the Schwinger–Keldysh formulation of nonequilibrium quantum field theory with the Nambu–Gor'kov formalism of quasiparticle excitations in the condensed phase and the tadpole method in quantum field theory. This method leads to causal equations of motion that allow us to study the nonequilibrium evolution as an initial value problem. It also allows us to extract directly the Ward identities, which are a consequence of the underlying gauge symmetry and which in equilibrium lead to the Hugenholtz–Pines theorem. An explicit one-loop calculation of the equations of motion beyond the Hartree–Fock–Bogoliubov approximation reveals that the nonlocal, absorptive contributions to the self-energies corresponding to the Beliaev and Landau damping processes are necessary to fulfill the Ward identities in or out of equilibrium. It is argued that a consistent implementation at low temperatures must be based on the loop expansion, which is shown to fulfill the Ward identities order by order in perturbation theory.

title: PROGRESS ON CHIRAL SYMMETRY BREAKING IN A STRONG MAGNETIC FIELD
abstract: The problem of chiral symmetry breaking in QED in a strong magnetic field is briefly reviewed. Recent progress on issues regarding the gauge fixing independence of the dynamically generated fermion mass is discussed.

title: REAL-TIME NONEQUILIBRIUM DYNAMICS IN HOT QED PLASMAS
abstract: The quantum kinetics of photons in hot QED plasmas is studied directly in real time by implementing the dynamical renormalization group. In contrast to conventional approach, the dynamical renormalization group method consistently includes off-shell (energy non-conserving) effects and accounts for time-dependent collisional kernel. To lowest order we find that in the relaxation time approximation the semihard photon distribution function relaxes with a power law.

title: Real time nonequilibrium dynamics in hot QED plasmas: Dynamical renormalization group approach
abstract: 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 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.

title: The Relationship between the Sudden Change of the Lorentz Force and the Magnitude of Associated Flares
abstract: The rapid and irreversible change of photospheric magnetic fields associated with flares has been confirmed by many recent studies. These studies showed that the photospheric magnetic fields respond to coronal field restructuring and turn to a more horizontal state near the magnetic polarity inversion line (PIL) after eruptions. Recent theoretical work has shown that the change in the Lorentz force associated with a magnetic eruption will lead to such a field configuration at the photosphere. The Helioseismic Magnetic Imager has been providing unprecedented full-disk vector magnetograms covering the rising phase of the solar cycle 24. In this study, we analyze 18 flares in four active regions, with GOES X-ray class ranging from C4.7 to X5.4. We find that there are permanent and rapid changes of magnetic field around the flaring PIL, the most notable of which is the increase of the transverse magnetic field. The changes of fields integrated over the area and the derived change of Lorentz force both show a strong correlation with flare magnitude. It is the first time that such magnetic field changes have been observed even for C-class flares. Furthermore, for seven events with associated coronal mass ejections (CMEs), we use an estimate of themore » impulse provided by the Lorentz force, plus the observed CME velocity, to estimate the CME mass. We find that if the timescale of the back reaction is short, i.e., in the order of 10 s, the derived values of CME mass ({approx}10{sup 15} g) generally agree with those reported in literature.« less

title: Unified field equations coupling four forces and principle of interaction dynamics
abstract: The main objective of this article is to postulate a principle of interaction dynamics (PID) and to derive field equations coupling the four fundamental interactions based on first principles. PID is a least action principle subject to div$_A$-free constraints for the variational element with $A$ being gauge potentials. The Lagrangian action is uniquely determined by 1) the principle of general relativity, 2) the $U(1)$, $SU(2)$ and $SU(3)$ gauge invariances, 3) the Lorentz invariance, and 4) the principle of representation invariance (PRI), introduced in . The unified field equations are then derived using PID. The field model spontaneously breaks the gauge symmetries, and gives rise to a new mass generation mechanism. 
The unified field model introduces a natural duality between the mediators and their dual mediators, and can be easily decoupled to study each individual interaction when other interactions are negligible. The unified field model, together with PRI and PID applied to individual interactions, provides clear explanations and solutions to a number of outstanding challenges in physics and cosmology, including e.g. the dark energy and dark matter phenomena, the quark confinement, asymptotic freedom, short-range nature of both strong and weak interactions, decay mechanism of sub-atomic particles, baryon asymmetry, and the solar neutrino problem.

title: Search for anomalous production of events with two photons and additional energetic objects at CDF
abstract: We present results of a search for anomalous production of two photons together with an electron, muon, τ lepton, missing transverse energy, or jets using pp collision data from 1.1–2.0  fb-1 of integrated luminosity collected by the Collider Detector at Fermilab (CDF). The event yields and kinematic distributions are examined for signs of new physics without favoring a specific model of new physics. The results are consistent with the standard model expectations. The search employs several new analysis techniques that significantly reduce instrumental backgrounds in channels with an electron and missing transverse energy.

title: Cosmological information in weak lensing peaks
abstract: Recent studies have shown that the number counts of convergence peaks N(kappa) in weak lensing (WL) maps, expected from large forthcoming surveys, can be a useful probe of cosmology. We follow up on this finding, and use a suite of WL convergence maps, obtained from ray-tracing N-body simulations, to study (i) the physical origin of WL peaks with different heights, and (ii) whether the peaks contain information beyond the convergence power spectrum P_ell. In agreement with earlier work, we find that high peaks (with amplitudes >~ 3.5 sigma, where sigma is the r.m.s. of the convergence kappa) are typically dominated by a single massive halo. In contrast, medium-height peaks (~0.5-1.5 sigma) cannot be attributed to a single collapsed dark matter halo, and are instead created by the projection of multiple (typically, 4-8) halos along the line of sight, and by random galaxy shape noise. Nevertheless, these peaks dominate the sensitivity to the cosmological parameters w, sigma_8, and Omega_m. We find that the peak height distribution and its dependence on cosmology differ significantly from predictions in a Gaussian random field. We directly compute the marginalized errors on w, sigma_8, and Omega_m from the N(kappa) + P_ell combination, including redshift tomography with source galaxies at z_s=1 and z_s=2. We find that the N(kappa) + P_ell combination has approximately twice the cosmological sensitivity compared to P_ell alone. These results demonstrate that N(kappa) contains non-Gaussian information complementary to the power spectrum.

title: Direct photon cross section with conversions at CDF
abstract: We present a measurement of the isolated direct photon cross section in pp collisions at {radical}(s)=1.8 TeV and |{eta}|<0.9 using data collected between 1994 and 1995 by the Collider Detector at Fermilab (CDF). The measurement is based on events where the photon converts into an electron-positron pair in the material of the inner detector, resulting in a two track event signature. To remove {pi}{sup 0}{yields}{gamma}{gamma} and {eta}{yields}{gamma}{gamma} events from the data we use a new background subtraction technique which takes advantage of the tracking information available in a photon conversion event. We find that the shape of the cross section as a function of photon p{sub T} is poorly described by next-to-leading-order QCD predictions, but agrees with previous CDF measurements.