Breakdown of the hard thermal loop expansion for quasi-real photons production

We discuss the bremsstrahlung production of soft real and virtual photons in a quark-gluon plasma at thermal equilibrium beyond the Hard Thermal Loop (HTL) resummation. The physics is controlled by the ratio $Q^{2}/q_{0}^{2}$ of the virtuality to the energy. When $Q^{2}/q_{0}^{2} ? g^{2}$ where g is the strong coupling constant, the emission rate is enhanced by a factor 1/g² over the HTL results due to light-cone singularities and the bremsstrahlung is induced by scattering of the quark via both transverse and longitudinal soft gluon exchanges. When $Q^{2}/q_{0}^{2}$ increases, the enhancement factor is given by $q_{0}^{2}/Q^{2}$. When this ratio is near unity, the bremsstrahlung contribution is of the same order as the rate predicted by the HTL resummation. In that case, the bremsstrahlung is induced by both soft and hard gluon exchanges.     

Soft photon production rate in resummed perturbation theory of high temperature QCD

We calculate the production rate of soft real photons from a hot quark-gluon plasma using Braaten-Pisarski's perturbative resummation method. To leading order in the QCD coupling constantg we find a logarithmically divergent result for photon energies of ordergT, whereT is the plasma temperature. This divergent behaviour is due to unscreened mass singularities in the effective hard thermal loop vertices in the case of a massless external photon.Laboratoire associé du Centre National de la Recherche Scientifique     

Calculation of Dielectric Function of a Quark-Gluon Plasma

With the hard thermal loop （HTL） resummation technique, we calculate the dielectric function excited by hard gluon in quark-gluon plasma （QCP）. We find that in a section of the space-like region po/p ∈ [0.78, 0.95], there are two extremum structures on the dielectric function curve, while the dielectric function in the HTL approximation decreases monotonously without these properties. Through the analyses of the imaginary part of the dielectric function, we conclude that the character of the dielectric function in this region reflects effects of the Landau damping.     

Non-abelian effects on wake potential in quark–gluon plasma

In this paper, based on the dielectric function calculated with the hard thermal loop (HTL) resummation approach, we study the wake potential induced by a fast parton traveling through quark–gluon plasma (QGP). In contrast to the wake potential calculated in the HTL approximation, our results show that non-abelian effects from the resummation calculation enhance the anisotropy of the wake potential. By investigating the relation between the anisotropic properties of the wake potential and the imaginary part of the dielectric function, we give some explanations for the enhancement of the anisotropy.     

Quark number susceptibility in hard thermal loop approximation

We calculate the quark number susceptibility in the deconfined phase of QCD using the hard thermal loop (HTL) approximation for the quark propagator and quark–meson vertices. This improved perturbation theory takes into account important medium effects such as thermal quark masses and Landau damping in the quark–gluon plasma. We explicitly show that the Landau damping part in the quark propagator for space-like quark momenta does not contribute to the quark number susceptibility due to the quark number conservation. We find that the quark number susceptibility only due to the collective quark modes deviates from the free one around the critical temperature but approaches free results in the infinite temperature limit. The results are in conformity with recent lattice calculations. Received: 7 December 2001 / Published online: 15 March 2002     

Resummation of large logarithms in the heavy-quark effects on the parton distributions inside the virtual photon

We discuss the resummation of the large logarithmic terms appearing in the heavy-quark effects on parton distribution functions inside the virtual photon. We incorporate heavy-quark mass effects by changing the initial condition of the leading-order DGLAP evolution equation. In a certain kinematical limit, we recover the logarithmic terms of the next-to-leading order heavy-quark effects obtained in the previous work. This method enables us to resum the large logarithmic terms due to heavy-quark mass effects on the parton distributions in the virtual photon. We numerically calculate parton distributions using the formulae derived in this work, and we discuss the property of the resummed heavy-quark effects.     

Vacuum Polarisation Effects in the Lorentz Violating Electrodynamics

In this work we reconsider the one loop calculation for the vacuum polarisation tensor in the Lorentz violating quantum electrodynamics. The electron propagator is “dressed” by a Lorentz breaking extra term in the fermion Lagrangian density. We check gauge invariance and use the Schwinger–Dyson equation to discuss the full photon propagator. After a discussion on a possible photon mass shift, we show how a finite quantum correction can be chosen in a unique way in order to ensure—in the spirit of spontaneously broken theories—the standard normalisation conditions for the vacuum polarisation tensor. Then we comment on possible observable physical consequences on the Lamb-shift.     

Comparing different hard-thermal-loop approaches to quark number susceptibilities

We compare our previously proposed hard-thermal-loop (HTL) resummed calculation of quark number susceptibilities using a self-consistent two-loop approximation to the quark density with a recent calculation of the same quantity at the one-loop level in a variant of HTL-screened perturbation theory. Besides pointing out conceptual problems with the latter approach, we show that it severely over-includes the leading-order interaction effects, while including none of the plasmon terms, which is the main reason for requiring improved resummation schemes. Received: 27 June 2002 / Revised version: 23 September 2002 / Published online: 31 January 2003     

Low Q^2 jet production at HERA in next-to-leading order QCD

We present next-to-leading order calculations of one- and two-jet production in eP collisions at HERA for photon virtualities in the range GeV. Soft and collinear singularities are extracted using the phase space slicing method. Numerical results are presented for HERA conditions with the Snowmass jet definition. The transition between photoproduction and deep-inelastic scattering is investigated in detail. We compare two approaches, the usual deep-inelastic theory, where the virtual photon couples only directly to quarks and antiquarks, and the photoproduction approach, where the photon couples either in the direct way or in the resolved way via the parton constituents of the virtual photon with the proton constituents. Finally we compare with recent H1 data of the dijet rate obtained for various photon virtualities with special attention to the region, in which two jets have equal transverse momenta. Received: 23 April 1998 / Published online: 26 August 1998     

Cusp Singularities in Boundary-Driven Diffusive Systems

Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be non-differentiable, a phenomenon that is unique to non-equilibrium systems, and discuss the types of models which display such singularities. The structure of these singularities is found to generically be a cusp, which can be described by a Landau free energy or, equivalently, by catastrophe theory. Connections with analogous results in systems with finite-dimensional phase spaces are drawn.     

Evaluation of laser-assisted bremsstrahlung with Dirac-Volkov propagators

We study spontaneous bremsstrahlung emission in a highly intense laser field. In this regime the interaction with the laser field has to be treated nonperturbatively by using the relativistic formalism including Dirac-Volkov propagators, while the interaction with the Coulomb field and the bremsstrahlung radiation can be treated in first-order perturbation theory. For the intermediate electron state a fully laser-dressed propagator is used, including radiative corrections to avoid singularities on the mass shell. We find that the use of the Dirac-Volkov propagator is crucial to obtain correct numerical results. The cross section of the process is evaluated for laser intensities of order 10(20) W/cm(2) and relativistic energies of the initial electron.     

The dilepton-production cross section in principal value resummation

Using a recent calculation of the perturbative hard part for dilepton production that sums large threshold corrections to all orders in perturbative QCD, we compute the corresponding cross sections. The hard part has been evaluated using principal value resummation and contains all singular momentum-dependent corrections. We also include a resummation of large Sudakov terms, which are independent of parton momenta. We give predictions for the dilepton-mass distribution, the rapidity distribution and the rapidity-integrated K-factor at fixed-target energies and compare with various experimental results in several kinematic regimes. We find that principal value resummation produces cross sections that are finite and well-behaved. For both protons and anti-protons on fixed targets, the resummed cross sections are, in general, in excellent agreement with the data.     

Propagator in a theory with confinement

We study the propagator in a model theory with confinement and attempt to show that, when summed to all orders, the propagator is free of singularities in the finite momentum plane. We find that Bethe-Salpeter ladder-like diagrams alone are insufficient to exhibit this behavior. However, in a non-relativistic approximation in the crossed channel, confinement is obtained and all poles disappear.     

Density-Density Propagator of the Luttinger Model of Spin-Half Fermions after an Interaction Quench

Motivated by recent research achievement of quantum interacting systems in non-equilibrium, we consider a Luttinger model with a suddenly switched-on interaction proposed by Cazalilla [M.A. Cazalilla, Phys. Rev. Lett. 97 (2006) 156403]. In order to compare with real systems, we extend Cazalilla's scenario to the spinful system. To find the influence of initial states on the time evolution of some non-equilibrium systems, we mainly focus on the density-density propagator. By comparison and analysis, we discover the different behavior of this non-equilibrium system. Further, it is found that the propagator saves strong memory of initial state, and the effects of right-left interaction cancel out in total density-density propagator.     

Density-Density Propagator of the Luttinger Model of Spin-Half Fermions after an Interaction Quench

Motivated by recent research achievement of quantum interacting systems in non-equilibrium, we consider a Luttinger model with a suddenly switched-on interaction proposed by Cazalilla [M.A. Cazalilla, Phys. Rev. Lett. 97 (2006) 156403]. In order to compare with real systems, we extend Cazalilla's scenario to the spinful system. To find the influence of initial states on the time evolution of some non-equilibrium systems, we mainly focus on the density-density propagator. By comparison and analysis, we discover the different behavior of this non-equilibrium system. Further, it is found that the propagator saves strong memory of initial state, and the effects of right-left interaction cancel out in total density-density propagator.     

Square-Root Operator Quantization and Nonlocality: A Review

A square-root-operator formalism is developed for quantum systems described with nonrelativistic and relativistic equations of motion. Spectral representation for Green's functions are designed for particles with spin 0, with the implication of its generalization to other spin values. Nonlocal operators suggest that a duality exists between physical particles and dual partners, which are tachyonic mathematical particles. It is shown that nonlocal operators result naturally from square-root operators, with the implication that microcausality holds only asymptotically. Applications help enlighten the formalism in order to envisage realistic situations with Schrödinger equations, Higgs fields, vacuum fluctuations, extra-dimensional methods in the potential theory, and electromagnetic interactions of extended charges and their consequences. It turns out that the innermost structure of these extended charges is associated with nonlocal photon propagators. It is shown that the propagator arisen from the charged torus potential consists of two different parts: a nonlocal photon propagator and a propagator of neutrino-like particles, which is described by square-root-operator equation. We examine the potential of the torus and its propagator as the appearance of superfields in terms of the photon and the massless fermion (photino).     

On de-globalization in quantum chromodynamics

The recent discovery and resummation of a class of single logarithmic effects (non-global logs), has a significant impact on several QCD observables ranging from the classic Sterman-Weinberg jet definition to currently studied event shapes and rapidity gap observables. The discovery of the above effects overturns, for example, the common wisdom that hadronic energy flow in limited inter-jet regions is dictatedprimarily by the colour flow of the underlying hard partonic subprocess. We discuss some features of non-global logs and the rapid progress being made in estimating and controlling such corrections.     

热密QED中的德拜质量

从QED中光子传播子的Schweinger-Dyson方程出发,得到一个有用的德拜质量和热力学压强之间的关系.利用这个关系以及有限温度与有限化学势下的相关压强计算了德拜质量的双圈修正.其结果显示双圈修正减少了德拜屏蔽质量.最后还讨论了QED等离子体中的磁质量     

Dissipative time evolution of observables in non-equilibrium statistical quantum systems

We discuss differential– versus integral–equation based methods describing out–of thermal equilibrium systems and emphasize the importance of a well defined reduction to statistical observables. Applying the projection operator approach, we investigate on the time evolution of expectation values of linear and quadratic polynomials in position and momentum for a statistical anharmonic oscillator with quartic potential. Based on the exact integro-differential equations of motion, we study the first and naive second order approximation which breaks down at secular time-scales. A method is proposed to improve the expansion by a non–perturbative resummation of all quadratic operator correlators consistent with energy conservation for all times. Motion cannot be described by an effective Hamiltonian local in time reflecting non-unitarity of the dissipative entropy generating evolution. We numerically integrate the consistently improved equations of motion for large times. We relate entropy to the uncertainty product, both being expressible in terms of the observables under consideration. Received: 21 July 1998 / Revised version: 28 September 1998 / Published online: 2 November 1998