Boosted Frames Research Articles

Relativity of the event: examples in JT gravity and linearized GR

Observables in quantum gravity are famously defined asymptotically, at the boundary of AdS or Minkowski spaces. However, by gauge fixing a coordinate system or suitably dressing the field operators, an approximate, “quasi-local” approach is also possible, that can give account of the measurements performed by a set of observers living inside the spacetime. In particular, one can attach spatial coordinates to the worldlines of these observers and use their proper times as a time coordinate. Here we highlight that any such local formulation has to face the relativity of the event, in that changing frame (= set of observers) implies a reshuffling of the point-events and the way they are identified. As a consequence, coordinate transformations between different frames become probabilistic in quantum gravity. We give a concrete realization of this mechanism in Jackiw-Teitelboim gravity, where a point in the bulk can be defined operationally with geodesics anchored to the boundary. We describe different ways to do so, each corresponding to a different frame, and compute the variances of the transformations relating some of these frames. In particular, we compute the variance of the location of the black hole horizon, which appears smeared in most frames. We then suggest how to calculate this effect in Einstein gravity, assuming knowledge of the wavefunction of the metric. The idea is to expand the latter on a basis of semiclassical states. Each element of this basis enjoys standard/deterministic coordinate transformations and the result is thus obtained by superposition. As a divertissement, we sabotage Lorentz boosts by adding to Minkoswki space a quantum superposition of gravitational waves and compute the probabilistic coordinate transformation to a boosted frame at linear order. Finally, we attempt to translate the relativity of the event into the language of dressed operators.

Particle production between isometric frames on a Poincaré patch of AdS2

In a recent paper [J. P. M. Pitelli, Phys. Rev. D 99, 108701 (2019)], one of us showed that the vacuum state associated with conformal fields on a Poincaré patch of anti-de Sitter spacetime is not AdS invariant for fields satisfying nontrivial boundary conditions (by nontrivial, we mean neither Dirichlet nor Neumann) at the conformal boundary. In this way, two isometrically related observers in anti-de Sitter space have different notions of no particle content. Therefore, an observer who is suddenly transported to a different (but isometrically related) frame will feel a bath of particles. This process contradicts our intuitive notion based on our experience in Minkowski spacetime, where the vacuum is Lorentz invariant, and no particle is produced between boosted frames. We show that the total number of produced particles is finite but grows without limit when we approach (via isometric transformation) Dirichlet or Neumann boundary conditions since in these cases the vacuum is invariant.

Accessing high-momentum nucleons with dilute stochastic sources

A novel stochastic technique combining a dilute source grid of noise with iterative momentum-smearing is used to study the proton correlation function at rest and in boosted frames on two lattice volumes. The technique makes use of the baryonic version of the so-called one-end trick, and the decomposition into signal and noise terms of the resulting stochastic proton correlation function is made explicit. The number and location of the source points in the dilute grid should be chosen so that the benefits of averaging over many locations overcomes the additional statistical error introduced by the noise terms in the desired fitting region. At all non-trivial momentum values considered we find that the choice of N = 4–8 maximally separated source locations is shown to be optimal, providing a reduced statistical error when compared with a single point source. This enables us to successfully fit the proton energy at momentum values as high as and on the small and large volume, respectively.

First law of entanglement entropy in topologically massive gravity

In this paper we explore the validity of the first law of entanglement entropy in the context of topologically massive gravity (TMG). We find that the variation of the holographic entanglement entropy under perturbation from the pure anti--de Sitter background satisfies the first law upon imposing the bulk equations of motion in a given time slice, despite the appearance of instabilities in the bulk for generic gravitational Chern-Simons coupling $\ensuremath{\mu}$. The Noether-Wald entropy is different from the holographic entanglement entropy in a general boosted frame. However, this discrepancy does not affect the entanglement first law.

Recent advances in high-performance modeling of plasma-based acceleration using the full PIC method

Numerical simulations have been critical in the recent rapid developments of plasma-based acceleration concepts. Among the various available numerical techniques, the particle-in-cell (PIC) approach is the method of choice for self-consistent simulations from first principles. The fundamentals of the PIC method were established decades ago, but improvements or variations are continuously being proposed. We report on several recent advances in PIC-related algorithms that are of interest for application to plasma-based accelerators, including (a) detailed analysis of the numerical Cherenkov instability and its remediation for the modeling of plasma accelerators in laboratory and Lorentz boosted frames, (b) analytic pseudo-spectral electromagnetic solvers in Cartesian and cylindrical (with azimuthal modes decomposition) geometries, and (c) novel analysis of Maxwell׳s solvers׳ stencil variation and truncation, in application to domain decomposition strategies and implementation of perfectly matched layers in high-order and pseudo-spectral solvers.

Boosted key-frame selection and correlated pyramidal motion-feature representation for human action recognition

In this paper we propose a novel method for human action recognition based on boosted key-frame selection and correlated pyramidal motion feature representations. Instead of using an unsupervised method to detect interest points, a Pyramidal Motion Feature (PMF), which combines optical flow with a biologically inspired feature, is extracted from each frame of a video sequence. The AdaBoost learning algorithm is then applied to select the most discriminative frames from a large feature pool. In this way, we obtain the top-ranked boosted frames of each video sequence as the key frames which carry the most representative motion information. Furthermore, we utilise the correlogram which focuses not only on probabilistic distributions within one frame but also on the temporal relationships of the action sequence. In the classification phase, a Support-Vector Machine (SVM) is adopted as the final classifier for human action recognition. To demonstrate generalizability, our method has been systematically tested on a variety of datasets and shown to be more effective and accurate for action recognition compared to the previous work. We obtain overall accuracies of: 95.5%, 93.7%, and 36.5% with our proposed method on the KTH, the multiview IXMAS and the challenging HMDB51 datasets, respectively.

Effects of hyperbolic rotation in Minkowski space on the modeling of plasma accelerators in a Lorentz boosted frame

The effects of hyperbolic rotation in Minkowski space resulting from the use of Lorentz boosted frames of calculation on laser propagation in plasmas are analyzed. Selection of a boost frame at the laser group velocity is shown to alter the laser spectrum, allowing the use of higher boost velocities. The technique is applied to simulations of laser driven plasma wakefield accelerators, which promise much smaller machines and whose development requires detailed simulations that challenge or exceed current capabilities. Speedups approaching the theoretical optima are demonstrated, producing the first direct simulations of stages up to 1 TeV. This is made possible by a million times speedup thanks to a frame boost with a relativistic factor γb as high as 1300, taking advantage of the rotation to mitigate an instability that limited previous work.

Modifications to Lorentz invariant dispersion in relatively boosted frames

We investigate the implications of energy-dependence of the speed of photons, one of the candidate effects of quantum-gravity theories that has been most studied recently, from the perspective of observations in different reference frames. We examine how a simultaneous burst of photons would be measured by two observers with a relative velocity, establishing some associated conditions for the consistency of theories. For scenarios where the Lorentz transformations remain valid these consistency conditions allow us to characterize the violations of Lorentz symmetry through an explicit description of the modification of the quantum-gravity scale in boosted frames with respect to its definition in a preferred frame. When applied to relativistic scenarios with a deformation of Lorentz invariance that preserves the equivalence of inertial observers, we find an insightful characterization of the necessity to adopt in such frameworks non-classical features of spacetime geometry, e.g. events that are at the same spacetime point for one observer cannot be considered at the same spacetime point for other observers. Our findings also suggest that, at least in principle (and perhaps one day even in practice), measurements of the dispersion of photons in relatively boosted frames can be particularly valuable for the purpose of testing these scenarios.

Modeling laser wakefield accelerator experiments with ultrafast particle-in-cell simulations in boosted frames

The development of new laser systems at the 10 Petawatt range will push laser wakefield accelerators to novel regimes, for which theoretical scalings predict the possibility to accelerate electron bunches up to tens of GeVs in meter-scale plasmas. Numerical simulations will play a crucial role in testing, probing, and optimizing the physical parameters and the setup of future experiments. Fully kinetic simulations are computationally very demanding, pushing the limits of today’s supercomputers. In this paper, the recent developments in the OSIRIS framework [R. A. Fonseca et al., Lect. Notes Comput. Sci. 2331, 342 (2002)] are described, in particular the boosted frame scheme, which leads to a dramatic change in the computational resources required to model laser wakefield accelerators. Results from one-to-one modeling of the next generation of laser systems are discussed, including the confirmation of electron bunch acceleration to the energy frontier.

Simulating relativistic beam and plasma systems using an optimal boosted frame

It was shown recently that it may be computationally advantageous to perform computer simulations in a Lorentz boosted frame for a certain class of systems. However, even if the computer model relies on a covariant set of equations, it was pointed out that algorithmic difficulties related to discretization errors may have to be overcome in order to take full advantage of the potential speedup. In this paper, we summarize the findings, the difficulties and their solutions, and review the applications of the technique that have been performed to date.

Space-times of boosted p-branes, and CFT in infinite-momentum frame

We study the space-times of the near-horizon regions in D3-brane, M2-brane and M5-brane configurations, in cases where there is a pp-wave propagating along a direction in the world-volume. While non-extremal configurations of this kind locally have the same Carter-Novotný-Horský-type metrics as those without the wave, taking the BPS limit results instead in Kaigorodov-type metrics, which are homogeneous, but preserve 1 4 of the supersymmetry, and have global and local structures that are quite different from the corresponding anti-de Sitter space-times associated with solutions where there is no pp-wave. We show that the momentum density of the system is non-vanishing and held fixed under the gravity decoupling limit. In view of the AdS/CFT correspondence, M-theory and type IIB theory in the near-horizon region of these boosted BPS-configurations specifies the corresponding CFT on the boundary in an infinitely boosted frame with constant momentum density. We model the microstates of such boosted configurations (which account for the microscopic counting of near-extremal black holes in D = 7, D = 9 and D = 6 by those of a boosted dilute massless gas in a d = 4, d = 3 and d = 6 space-time respectively. Thus we obtain a simple description for the entropy of 2-charge black holes in D = 7, 9 and 6 dimensions. The paper includes constructions of generalisations of the Kaigorodov and Carter-Novotný-Horský metrics in arbitrary space-time dimensions, and an investigation of their properties.