Forward Light Cone Research Articles

Positivity bounds on electromagnetic properties of media

We study the constraints imposed on the electromagnetic response of general media by microcausality (commutators of local fields vanish outside the light cone) and positivity of the imaginary parts (the medium can only absorb energy from the external field). The equations of motion for the average electromagnetic field in a medium — the macroscopic Maxwell equations — can be derived from the in-in effective action and the effect of the medium is encoded in the electric and magnetic permeabilities ε(ω, |k|) and μ(ω, |k|). Microcausality implies analyticity of the retarded Green’s functions when the imaginary part of the 4-vector (ω, k) lies in forward light cone. With appropriate assumptions about the behavior of the medium at high frequencies one derives dispersion relations, originally studied by Leontovich. In the case of dielectrics these relations, combined with the positivity of the imaginary parts, imply bounds on the low-energy values of the response, ε(0, 0) and μ(0, 0). In particular the quantities ε(0, 0) – 1 and ε(0, 0) – 1/μ(0, 0) are constrained to be positive and equal to integrals over the imaginary parts of the response. We discuss various improvements of these bounds in the case of non-relativistic media and with additional assumptions about the UV behavior.

Where Charged Sectors are Localizable: A Viewpoint from Covariant Cohomology

Given a Haag–Kastler net on a globally hyperbolic spacetime, one can consider a family of regions where quantum charges are supposed to be localized. Assuming that the net fulfils certain minimal properties (factoriality of the global observable algebra and relative Haag duality), we give a geometric criterion that the given family must fulfil to have a superselection structure with charges localized on its regions. Our criterion is fulfilled by all the families used in the theory of sectors (double cones, spacelike cones, diamonds, hypercones). In order to take account of eventual spacetime symmetries, our superselection structures are constructed in terms of covariant charge transporters, a novel cohomological approach generalizing that introduced by J. E. Roberts. In the case of hypercones, with the forward light cone as an ambient spacetime, we obtain a superselection structure with Bose–Fermi parastatistics and particle-antiparticle conjugation. It could constitute a candidate for a different description of the charged sectors introduced by Buchholz and Roberts for theories including massless particles.

XUV Fluorescence Detection of Laser-Cooled Stored Relativistic Ions

An improved moveable in vacuo XUV fluorescence detection system was employed for the laser cooling of bunched relativistic (β = 0.47) carbon ions at the Experimental Storage Ring (ESR) of GSI Helmholtzzentrum Darmstadt, Germany. Strongly Doppler boosted XUV fluorescence (∼90 nm) was emitted from the ions in a forward light cone after laser excitation of the 2s–2p transition (∼155 nm) by a new tunable pulsed UV laser system (257 nm). It was shown that the detected fluorescence strongly depends on the position of the detector around the bunched ion beam and on the delay (∼ns) between the ion bunches and the laser pulses. In addition, the fluorescence information could be directly combined with the revolution frequencies of the ions (and their longitudinal momentum spread), which were recorded using the Schottky resonator at the ESR. These fluorescence detection features are required for future laser cooling experiments at highly relativistic energies (up to γ∼ 13) and high intensities (up to 1011 particles) of ion beams in the new heavy ion synchrotron SIS100 at FAIR.

Scalar and vector tail radiation from the interior of the lightcone

In a generic spacetime a massless field propagates not just on the surface of the forward lightcone of a source, but in its interior. This inside-the-lightcone “tail radiation” is often described as having “scattered” off the spacetime curvature. In this work, we study the propagation of such tail radiation for a compact, static, spherically symmetric weak-field (i.e. low density) mass distribution that is well off the line-of-sight (LOS) between a source and an observer, and that is coupled to the radiation only gravitationally. For such perturbers, there are four distinct epochs in the observed radiation: the light-cone piece; the subsequent early-time tail—ending at the first time that a signal moving at the speed of light could travel from the source to a point in the perturber thence to the observer; the subsequent middle-time tail; and the late-time tail, beginning at the last time that a signal could make such a journey. For massless scalar and vector (eg. electromagnetic radiation), we revisit the previously studied early and late-time tail, and perform the first full examination of the middle-time tail. Studying shorter wavelengths and generic perturbers well off the LOS, we find that the late-time tail carries a small fraction of the energy received by the observer; however, the total middle-time tail contains much more energy. We also note that whereas the middle-time tail appears to the observer to emanate from the perturber—as one might expect for radiation “scattered” from the gravitational perturbation—the late-time tail appears to come back from the source. We speculate on the potential utility of this middle-time tail for detecting or probing a wide variety of perturbations to the spacetime geometry including dark matter candidates and dark matter halos.

Second gradient electrodynamics: Green functions, wave propagation, regularization and self-force

In this work, the theory of second gradient electrodynamics, which is an important example of generalized electrodynamics, is proposed and investigated. Second gradient electrodynamics is a gradient field theory with up to second-order derivatives of the electromagnetic field strengths in the Lagrangian density. Second gradient electrodynamics possesses a weak nonlocality in space and time. In the framework of second gradient electrodynamics, the retarded Green functions, first-order derivatives of the retarded Green functions, retarded potentials, retarded electromagnetic field strengths, generalized Liénard–Wiechert potentials and the corresponding electromagnetic field strengths are derived for three, two and one spatial dimensions. The behaviour of the electromagnetic fields is investigated on the light cone. In particular, the retarded Green functions and their first-order derivatives show oscillations around the classical solutions inside the forward light cone and it is shown that they are singularity-free and regular on the light cone in three, two and one spatial dimensions. In second gradient electrodynamics, the self-force and the energy release rate are calculated and the equation of motion of a charged point particle, which is an integro-differential equation where the infamous third-order time-derivative of the position does not appear, is determined.

Green functions and propagation in the Bopp–Podolsky electrodynamics

In this paper, we investigate the so-called Bopp–Podolsky electrodynamics. The Bopp–Podolsky electrodynamics is a prototypical gradient field theory with weak nonlocality in space and time. The Bopp–Podolsky electrodynamics is a Lorentz and gauge invariant generalization of the Maxwell electrodynamics. We derive the retarded Green functions, first derivatives of the retarded Green functions, retarded potentials, retarded electromagnetic field strengths, generalized Liénard–Wiechert potentials and the corresponding electromagnetic field strengths in the framework of the Bopp–Podolsky electrodynamics for three, two and one spatial dimensions. We investigate the behaviour of these electromagnetic fields in the neighbourhood of the light cone. In the Bopp–Podolsky electrodynamics, the retarded Green functions and their first derivatives show fast decreasing oscillations inside the forward light cone.

Relativistic Markovian dynamical collapse theories must employ nonstandard degrees of freedom

The impossibility of an indeterministic evolution for standard relativistic quantum field theories, that is, theories in which all fields satisfy the condition that the generators of spacetime translation have spectrum in the forward light-cone, is demonstrated. The demonstration proceeds by arguing that a relativistically invariant theory must have a stable vacuum, and then showing that stability of the vacuum, together with the requirements imposed by relativistic causality, entails deterministic evolution, if all degrees of freedom are standard degrees of freedom.

Profiles for the Radial Focusing 4d Energy-Critical Wave Equation

Consider a finite energy radial solution to the focusing energy critical semilinear wave equation in 1 + 4 dimensions. Assume that this solution exhibits type-II behavior, by which we mean that the critical Sobolev norm of the evolution stays bounded on the maximal interval of existence. We prove that along a sequence of times tending to the maximal forward time of existence, the solution decomposes into a sum of dynamically rescaled solitons, a free radiation term, and an error tending to zero in the energy space. If, in addition, we assume that the critical norm of the evolution localized to the light cone (the forward light cone in the case of global solutions and the backwards cone in the case of finite time blow-up) is less than 2 times the critical norm of the ground state solution W, then the decomposition holds without a restriction to a subsequence.

A Novel Approach For Event-By-Event Early Gluon Fields

We report on efforts to construct an event generator that calculates the classical gluon field generated at early times in high energy nuclear collisions. Existing approaches utilize numerical solutions of the Yang-Mills equations after the collision. In contrast we employ the analytically known recursion relation in the forward light cone. The few lowest orders are expected to lead to reliable results for times of up to the inverse saturation scale, τ0∼1/Qs. In these proceedings we sketch some calculational details, and show some preliminary results.

Structure of longitudinal chromomagnetic fields in high energy collisions

We compute expectation values of spatial Wilson loops in the forward light cone of high-energy collisions. We consider ensembles of gauge field configurations generated from a classical Gaussian effective action as well as solutions of high-energy renormalization group evolution with fixed and running coupling. The initial fields correspond to a color field condensate exhibiting domain-like structure over distance scales of order the saturation scale. At later times universal scaling emerges at large distances for all ensembles, with a nontrivial critical exponent. Finally, we compare the results for the Wilson loop to the two-point correlator of magnetic fields.

Spatial Wilson loops in the classical field of high-energy heavy-ion collisions

It has been previously shown numerically that the expectation value of the magnetic Wilson loop at the initial time of a heavy-ion collision exhibits area law scaling. This was obtained for a classical non-Abelian gauge field in the forward light cone and for loops of area $A\gtrsim 2/Q_s^2$. Here, we present an analytic calculation of the spatial Wilson loop in the classical field of a collision within perturbation theory. It corresponds to a diagram with two sources, for both projectile and target, whose field is evaluated at second order in the gauge potential. The leading non-trivial contribution to the magnetic loop in perturbation theory is proportional to the square of its area.

Magnetic flux loop in high-energy heavy-ion collisions

We consider the expectation value of a magnetic flux loop in the immediate forward light cone of collisions of heavy nuclei at high energies. Such collisions are characterized by a non-linear scale Q_s where color fields become strong. We find that loops of area greater than ~2/Q_s^2 exhibit area law behavior, which determines the scale of elementary flux excitations ("vortices"). We also estimate the magnetic string tension, sigma_M = 0.12 Q_s^2. By the time t ~ 1/Q_s even small loops satisfy an area law. We describe corrections to the propagator of semi-hard gluons at very early times in the background of fluctuating magnetic fields.

Point-form dynamics of quasistable states

We present a field theoretical model of point-form dynamics which exhibits resonance scattering. In particular, we construct point-form Poincaré generators explicitly from field operators and show that in the vector spaces for the in-states and out-states (endowed with certain analyticity and topological properties suggested by the structure of the S-matrix) these operators integrate to furnish differentiable representations of the causal Poincaré semigroup, the semidirect product of the semigroup of spacetime translations into the forward lightcone and the group of Lorentz transformations. We also show that there exists a class of irreducible representations of the Poincaré semigroup defined by a complex mass and a half-integer spin. The complex mass characterizing the representation naturally appears in the construction as the square root of the pole position of the propagator. These representations provide a description of resonances in the same vein as Wigner's unitary irreducible representations of the Poincaré group provide a description of stable particles.

Morawetz estimates for the wave equation at low frequency

We consider Morawetz estimates for weighted energy decay of solutions to the wave equation on scattering manifolds (i.e., those with large conic ends). We show that a Morawetz estimate persists for solutions that are localized at low frequencies, independent of the geometry of the compact part of the manifold. We further prove a new type of Morawetz estimate in this context, with both hypotheses and conclusion localized inside the forward light cone. This result allows us to gain a $$1/2$$ power of $$t$$ decay relative to what would be dictated by energy estimates, in a small part of spacetime.

Quantization of propagating modes in optical fibres

The electromagnetic fields of a single optic fibre mode are quantized based on the observation that these fields can be derived from a scalar harmonic oscillator function depending on only time and the axial wavenumber. Asymptotic results for both the one-photon probability density and two-photon correlation density functions within the forward light cone are presented, showing an algebraic decay for large times or distances. This algebraic decay, increasing the uncertainty in the arrival time of the photons, also remains in the presence of dispersion shift, in qualitative agreement with experimental results. Also presented are explicit formulae to be used in parameter studies to optimize quantum optic fibre communications.

Heavy ion collisions in AdS 5

We study heavy ion collisions at strong ʼt Hooft coupling using AdS/CFT correspondence. Heavy ion collisions correspond to gravitational shock wave collisions in AdS 5. We construct the metric in the forward light cone after the collision perturbatively through expansion of Einstein equations in graviton exchanges. We obtain an analytic expression for the metric including all-order graviton exchanges with one shock wave, while keeping the exchanges with another shock wave at the lowest order. We read off the corresponding energy-momentum tensor of the produced medium. Unfortunately this energy-momentum tensor does not correspond to ideal hydrodynamics, indicating that higher order graviton exchanges are needed to construct the full solution of the problem. We also show that shock waves must completely stop almost immediately after the collision in AdS 5, which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Finally, we perform trapped surface analysis of the shock wave collisions demonstrating that a bulk black hole, corresponding to ideal hydrodynamics on the boundary, has to be created in such collisions, thus constructing a proof of thermalization in heavy ion collisions at strong coupling.

Anomalous Cherenkov spin-orbit sound

The Cherenkov effect is a well known phenomenon in the electrodynamics of fast charged particles passing through transparent media. If the particle is faster than the light in a given medium, the medium emits a forward light cone. This beautiful phenomenon has an acoustic counterpart where the role of photons is played by phonons and the role of the speed of light is played by the sound velocity. In this case the medium emits a forward sound cone. Here, we show that in a system with spin-orbit interactions in addition to this {\it normal} Cherenkov sound there appears an {\it anomalous} Cherenkov sound with forward and {\it backward} sound propagation. Furthermore, we demonstrate that the transition from the normal to anomalous Cherenkov sound happens in a {\it singular} way at the Cherenkov cone angle. The detection of this acoustic singularities therefore represents an alternative experimental tool for the measurement of the spin-orbit coupling strength.

Pair creation in boost-invariantly expanding electric fields and two-particle correlations

Pair creation of scalar particles in a boost-invariant electric field which is confined in the forward light cone is studied. We present the proper-time evolution of momentum distributions of created particles, which preserve the boost invariance of the background field. The two-particle correlation of the created particles is also calculated. We find that long-range rapidity correlations may arise from the Schwinger mechanism in the boost-invariant electric field.

Coorbit spaces for dual pairs

In this paper we present an abstract framework for construction of Banach spaces of distributions from group representations. This extends the theory of coorbit spaces initiated by H.G. Feichtinger and K. Gröchenig in the 1980s. The coorbit theory sets up a correspondence between spaces of distributions and reproducing kernel Banach spaces. The original theory required that the initial representation was irreducible, unitary and integrable. As a consequence not all Bergman spaces could be described as coorbits. Our approach relies on duality arguments, which are often verifiable in cases where integrability fails. Moreover it does not require the representation to be irreducible or even come from a unitary representation on a Hilbert space. This enables us to account for the full Banach-scale of Bergman spaces on the unit disk for which we also provide atomic decompositions. Replacing the integrability criteria with duality also has the advantage that the reproducing kernel need not provide a continuous projection from a larger Banach function space. We finish the article with a wavelet characterization of Besov spaces on the forward light cone.

Shock Wave Collisions and Thermalization in AdS5

We study heavy ion collisions at strong 't Hooft coupling using AdS/CFT correspondence. According to the AdS/CFT dictionary heavy ion collisions correspond to gravitational shock wave collisions in AdS_5. We construct the metric in the forward light cone after the collision perturbatively through expansion of Einstein equations in graviton exchanges. We obtain an analytic expression for the metric including all-order graviton exchanges with one shock wave, while keeping the exchanges with another shock wave at the lowest order. We read off the corresponding energy-momentum tensor of the produced medium. Unfortunately this energy-momentum tensor does not correspond to ideal hydrodynamics, indicating that higher order graviton exchanges are needed to construct the full solution of the problem. We also show that shock waves must completely stop almost immediately after the collision in AdS_5, which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Finally, we perform trapped surface analysis of the shock wave collisions demonstrating that a bulk black hole, corresponding to ideal hydrodynamics on the boundary, has to be created in such collisions, thus constructing a proof of thermalization in heavy ion collisions at strong coupling.