Thomas Heinzl

Light-Cone Quantization: Foundations and Applications

These lecture notes review the foundations and some applications of light-cone quantization. First I explain how to choose a time in special relativity. Inclusion of Poincare invariance naturally leads to Dirac’s forms of relativistic dynamics. Among these, the front form, being the basis for light-cone quantization, is my main focus. I explain a few of its peculiar features such as boost and Galilei invariance or separation of relative and center-of-mass motion. Combining light-cone dynamics and field quantization results in light-cone quantum field theory. As the latter represents a first-order system, quantization is somewhat nonstandard. I address this issue using Schwinger’s quantum action principle, the method of Faddeev and Jackiw, and the functional Schrodinger picture. A finite-volume formulation, discretized light-cone quantization, is analysed in detail. I point out some problems with causality, which are absent in infinite volume. Finally, the triviality of the light-cone vacuum is established. Coming to applications, I introduce the notion of light-cone wave functions as the solutions of the light-cone Schrodinger equation. I discuss some examples, among them nonrelativistic Coulomb systems and model field theories in two dimensions. Vacuum properties (like chiral condensates) are reconstructed from the particle spectrum obtained by solving the light-cone Schrodinger equation. In a last application, I make contact with phenomenology by calculating the pion wave function within the Nambu and Jona-Lasinio model. I am thus able to predict a number of observables like the pion charge and core radius, the r.m.s. transverse momentum, the pion structure function and the pion distribution amplitude. The latter turns out to be the asymptotic one.

Signatures of high-intensity Compton scattering

We review known and discuss new signatures of high-intensity Compton scattering assuming a scenario where a high-power laser is brought into collision with an electron beam. At high intensities one expects to see a substantial redshift of the usual kinematic Compton edge of the photon spectrum caused by the large, intensity-dependent effective mass of the electrons within the laser beam. Emission rates acquire their global maximum at this edge while neighboring smaller peaks signal higher harmonics. In addition, we find that the notion of the center-of-mass frame for a given harmonic becomes intensity dependent. Tuning the intensity then effectively amounts to changing the frame of reference, going continuously from inverse to ordinary Compton scattering with the center-of-mass kinematics defining the transition point between the two.

Finite size effects in stimulated laser pair production

We consider stimulated pair production employing strong-field QED in a high-intensity laser background. In an infinite plane wave, we show that light-cone quasi-momentum can only be transferred to the created pair as a multiple of the laser frequency, i.e. by a higher harmonic. This translates into discrete resonance conditions providing the support of the pair creation probability which becomes a delta-comb. These findings corroborate the usual interpretation of multi-photon production of pairs with an effective mass. In a pulse, the momentum transfer is continuous, leading to broadening of the resonances and sub-threshold behaviour. The peaks remain visible as long as the number of cycles per pulse exceeds unity. The resonance patterns in pulses are analogous to those of a diffraction process based on interference of the produced pairs. We finally comment on the dependence of the peak positions, and in turn the effective mass, on the pulse shape.

Beam-shape effects in nonlinear Compton and Thomson scattering

We discuss intensity effects in collisions between beams of optical photons from a high-power laser and relativistic electrons. Our main focus is on the modifications of the emission spectra due to realistic finite-beam geometries. By carefully analyzing the classical limit we precisely quantify the distinction between strong-field QED Compton scattering and classical Thomson scattering. A purely classical, but fully covariant, calculation of the bremsstrahlung emitted by an electron in a plane-wave laser field yields radiation into harmonics, as expected. This result is generalized to pulses of finite duration and explains the appearance of line broadening and harmonic substructure as an interference phenomenon. The ensuing numerical treatment confirms that strong focusing of the laser leads to a broad continuum while higher harmonics become visible only at moderate focusing, and hence lower intensity. We present a scaling law for the backscattered photon spectral density which facilitates averaging over electron beam phase space. Finally, we propose a set of realistic parameters such that the observation of intensity-induced spectral red shift, higher harmonics, and their substructure becomes feasible.

Exploring high-intensity QED at ELI

We give a non-technical overview of QED effects arising in the presence of ultra-strong electromagnetic fields highlighting the new prospects provided by a realisation of the ELI laser facility.

A Lorentz and gauge invariant measure of laser intensity

Focussing on null fields as simple models of laser beams we discuss the classical relativistic motion of charges in strong electromagnetic fields. We suggest a universal, Lorentz and gauge invariant measure of laser intensity and explicitly calculate and interpret it for crossed field, plane wave and vortex models.

Inverse Monte-Carlo determination of effective lattice models for SU(3) Yang-Mills theory at finite temperature

This paper concludes our efforts in describing

Phase structure of Z(3)-Polyakov-loop models

SU(3)

Intensity-Dependent Electron Mass Shift in a Laser Field: Existence, Universality, and Detection

-Yang-Mills theories at different couplings/temperatures in terms of effective Polyakov-loop models. The associated effective couplings are determined through an inverse Monte Carlo procedure based on novel Schwinger-Dyson equations that employ the symmetries of the Haar measure. Because of the first-order nature of the phase transition we encounter a fine-tuning problem in reproducing the correct behavior of the Polyakov-loop from the effective models. The problem remains under control as long as the number of effective couplings is sufficiently small.

Symmetry breaking from radiation reaction in ultra-intense laser fields

We study effective lattice actions describing the Polyakov-loop dynamics originating from finite-temperature Yang-Mills theory. Starting with a strong-coupling expansion the effective action is obtained as a series of Z(3)-invariant operators involving higher and higher powers of the Polyakov loop, each with its own coupling. Truncating to a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean-field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both approaches concerning the phase structure of the theories. The phase diagram exhibits both first and second order transitions between symmetric, ferromagnetic, and antiferromagnetic phases with phase boundaries merging at three tricritical points. The critical exponents {nu} and {gamma} at the continuous transition between symmetric and antiferromagnetic phases are the same as for the 3-state Potts model.