Strong-field effects in laboratory and astrophysical plasmas and high intensity laser and cavity systems are considered, related to quantum electrodynamical (QED) photon-photon scattering. Current state-of-the-art laser facilities are close to reaching energy scales at which laboratory astrophysics will become possible. In such high energy density laboratory astrophysical systems, quantum electrodynamics will play a crucial role in the dynamics of plasmas and indeed the vacuum itself. Developments such as the free-electron laser may also give a means for exploring remote violent events such as supernovae in a laboratory environment. At the same time, superconducting cavities have steadily increased their quality factors, and quantum nondemolition measurements are capable of retrieving information from systems consisting of a few photons. Thus, not only will QED effects such as elastic photon-photon scattering be important in laboratory experiments, it may also be directly measurable in cavity experiments. Here implications of collective interactions between photons and photon-plasma systems are described. An overview of strong field vacuum effects is given, as formulated through the Heisenberg-Euler Lagrangian. Based on the dispersion relation for a single test photon traveling in a slowly varying background electromagnetic field, a set of equations describing the nonlinear propagation of an electromagnetic pulse on a radiation plasma is derived. The stability of the governing equations is discussed, and it is shown using numerical methods that electromagnetic pulses may collapse and split into pulse trains, as well as be trapped in a relativistic electron hole. Effects, such as the generation of novel electromagnetic modes, introduced by QED in pair plasmas is described. Applications to laser-plasma systems and astrophysical environments are also discussed.

Nonlinear collective effects in photon-photon and photon-plasma interactions

Mes premiers remtrciements trout aux auteurs des 206 communications th6matiquts et notes de projet, sans qui ces actes n'auraient 6videmment pas vu le jour. / Is oat contribu6 h la qualit6 scientifique et ,5 I'hmuog6t~6it6 pr6sentationntlle de leurs articles en refondant les versions iuitiales soumises an comit6 de programme, ea acceptant de suivre les r~gles de pr6sentation indiqu6es, et en nous envoyant parrots plusieurs versions am61ior6es surun point ou sur l'autrc.

/pdf/about-these-proceedings-4s0qpzq930.pdf

About these proceedings

Progress in particle and nuclear physics

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory. For decades it has been a dream to study these intricate strongly coupled theories nonperturbatively using symmetries and other consistency conditions. This idea, called the conformal bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been fully realized in three, four, and other dimensions of interest. This renaissance has been possible both due to significant analytical progress in understanding how to set up the bootstrap equations and the development of numerical techniques for finding or constraining their solutions. These developments have led to a number of groundbreaking results, including world record determinations of critical exponents and correlation function coefficients in the Ising and $O(N)$ models in three dimensions. This article will review these exciting developments for newcomers to the bootstrap, giving an introduction to conformal field theories and the theory of conformal blocks, describing numerical techniques for the bootstrap based on convex optimization, and summarizing in detail their applications to fixed points in three and four dimensions with no or minimal supersymmetry.

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications

These notes are an updated version of lectures given at the Cours de Troisieme Cycle de la Physique en Suisse Romande (Lausanne, Switzerland) in June 1989. We thank the Troisieme Cycle de la Physique en Suisse Romande and Professor Michel Droz for kindly giving permission to reprint these notes.

Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms

We investigate the mechanism of pair creation in scalar QED from spatially homogeneous strong electric fields in 1+1 dimensions. Solution of the semiclassical field equations shows particle creation followed by plasma oscillations. We compare our results with a model based on a relativistic Boltzmann-Vlasov equation with a pair-creation source term related to the Schwinger mechanism. The time evolution of the electric field and the current obtained from the Boltzmann-Vlasov model is surprisingly similar to that found in the semiclassical calculation.

Pair production in a strong electric field.

The initial-value problem for the quantum back reaction in spinor QED is formulated and solved in the semiclassical mean-field approximation for a homogeneous but time-dependent electric field $E(t)$. We apply the method of adiabatic regularization to the Dirac equation in order to renormalize the expectation value of the current and derive a finite coupled set of ordinary differential equations for the time evolution of the system. We solve this system in 1+1 dimensions numerically and compare the solution to a simple model based on a relativistic Boltzmann-Vlasov equation, with a particle production source term inferred from the Schwinger particle creation rate and a Pauliblocking factor. This model reproduces very well the time behavior of the electric field and the creation rate of ${e}^{+}{e}^{\ensuremath{-}}$ pairs of the semiclassical calculation.

Fermion pair production in a strong electric field.

We have carried out a Schrodinger functional calculation for the SU(3) lattice gauge theory with two flavors of Wilson fermions in the sextet representation of the gauge group. We find that the discrete beta function, which governs the change in the running coupling under a discrete change of spatial scale, changes sign when the Schrodinger functional renormalized coupling is in the neighborhood of g{sup 2}=2.0. The simplest explanation is that the theory has an infrared-attractive fixed point, but more complicated possibilities are allowed by the data. While we compare rescalings by factors of 2 and 4/3, we work at a single lattice spacing.

Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions

We apply Schroedinger-functional techniques to the SU(2) lattice gauge theory with N{sub f}=2 flavors of fermions in the adjoint representation. Our use of hypercubic smearing enables us to work at stronger couplings than did previous studies, before encountering a critical point and a bulk phase boundary. Measurement of the running coupling constant gives evidence of an infrared fixed point g{sub *} where 1/g{sub *}{sup 2}=0.20(4)(3). At the fixed point, we find a mass anomalous dimension {gamma}{sub m}(g{sub *})=0.31(6).

Infrared fixed point in SU(2) gauge theory with adjoint fermions

We have performed numerical simulations of SU(3) gauge theory coupled to ${N}_{f}=2$ flavors of symmetric-representation fermions. The fermions are discretized with the tadpole-improved clover action. Our simulations are done on lattices of length $L=6$, 8, and 12. In all simulation volumes we observe a crossover from a strongly coupled confined phase to a weak-coupling deconfined phase. Degeneracies in screening masses, plus the behavior of the pseudoscalar decay constant, indicate that the deconfined phase is also a phase in which chiral symmetry is restored. The movement of the confinement transition as the volume is changed is consistent with avoidance of the basin of attraction of an infrared fixed point of the massless theory.

Benjamin Svetitsky

Papers

Pair production in a strong electric field.

Fermion pair production in a strong electric field.

Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions

Infrared fixed point in SU(2) gauge theory with adjoint fermions

Phase structure of SU(3) gauge theory with two flavors of symmetric-representation fermions