All Stable Characteristic Classes of Homological Vector Fields

An odd vector field $Q$ on a supermanifold $M$ is called homological, if $Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra of smooth tensor fields on $M$ into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator $L_Q$ and are represented by $Q$-invariant tensors made up of the homological vector field and a symmetric connection on $M$ by means of tensor operations.Comment: 17 pages, references and comments adde

Photon polarization tensor in circularly polarized Hermite- and Laguerre-Gaussian beams

We derive analytical expressions for the photon polarization tensor in circularly polarized Hermite- and Laguerre-Gaussian beams, complementing the corresponding results for linearly polarized beams obtained recently. As they are based upon a locally constant field approximation of the one-loop Heisenberg-Euler effective Lagrangian for quantum electrodynamics (QED) in constant fields, our results are generically limited to slowly varying electromagnetic fields, varying on spatial (temporal) scales much larger than the Compton wavelength (time) of the electron.Comment: 6 pages; Contribution to the LPHYS'17 Conference Proceeding

X-ray photon scattering at a focused high-intensity laser pulse

We study x-ray photon scattering in the head-on collision of an XFEL pulse and a focused high-intensity laser pulse, described as paraxial Laguerre-Gaussian beam of arbitrary mode composition. For adequately chosen relative orientations of the polarization vectors of the colliding laser fields, this gives rise to a vacuum birefringence effect manifesting itself in polarization flipped signal photons. Throughout this article the XFEL is assumed to be mildly focused to a waist larger than that of the high-intensity laser beam. As previously demonstrated for the special case of a fundamental paraxial Gaussian beam, this scenario is generically accompanied by a scattering phenomenon of x-ray energy signal photons outside the forward cone of the XFEL beam, potentially assisting the detection of the effect in experiment. Here, we study the fate of the x-ray scattering signal under exemplary deformations of the transverse focus profile of the high-intensity pump.Comment: 21 pages, 3 figure

Photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian beams

In this article, we provide analytical expressions for the photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian laser beams. Our results are based on a locally constant field approximation of the one-loop Heisenberg-Euler effective Lagrangian for quantum electrodynamics. Hence, by construction they are limited to slowly varying electromagnetic fields, varying on spatial and temporal scales significantly larger than the Compton wavelength/time of the electron. The latter criterion is fulfilled by all laser beams currently available in the laboratory. Our findings will, e.g., be relevant for the study of vacuum birefringence experienced by probe photons brought into collision with a high-intensity laser pulse which can be represented as a superposition of either Hermite- or Laguerre-Gaussian modes.Comment: 18 pages, 1 figur

Enhancing quantum vacuum signatures with tailored laser beams

We demonstrate that tailored laser beams provide a powerful means to make quantum vacuum signatures in strong electromagnetic fields accessible in experiment. Typical scenarios aiming at the detection of quantum vacuum nonlinearities at the high-intensity frontier envision the collision of focused laser pulses. The effective interaction of the driving fields mediated by vacuum fluctuations gives rise to signal photons encoding the signature of quantum vacuum nonlinearity. Isolating a small number of signal photons from the large background of the driving laser photons poses a major experimental challenge. The main idea of the present work is to modify the far-field properties of a driving laser beam to exhibit a field-free hole in its center, thereby allowing for an essentially background free measurement of the signal scattered in the forward direction. Our explicit construction makes use of a peculiar far-field/focus duality.Comment: 5 pages, 3 figures; presentation improved, matches PRD versio