arXiv subjects

Jordan Wilson-Gerow

Publications and source records attributed to Jordan Wilson-Gerow.

16 recordsLinked to original sources

arXiv2026

A Unified Treatment of the Self-Force Problem

This paper introduces formalism, based on worldline effective field theory, which allows one to systematically calculate the gravitational self-force on a compact object immersed in an environment with non-vanishing stress energy. Using the closed time path integral we present a universal effective action that can be used to calculate the equations of motion of a compact object due to its interaction with the environment to any order in the relevant expansion parameters, the relative importance of which depends upon the choice of environment. We show that the leading order equations of motion can be universally written in terms of the retarded two-point function of the stress-energy tensor for the environment. The resulting action can be used to calculate both dissipative (dynamical friction) and conservative forces in a completely relativistic fashion. We demonstrate the utility of the result by calculating the dissipative force due to dust, an inviscid fluid, and a coherent field. Our results agree with those previously derived in the literature. We furthermore show that the famous ``Coulomb Log" found by Chandrasekhar should be interpreted as a renormalization group log due to a UV divergence that renormalizes the dissipative part of the in-in action. We then prove that this log is universal in the Newtonian limit in that its value is universal, for a generic class of environments and trajectories. This log is the leading log in an RG flow in the dissipative action that has yet to be explored.

gr-qc↗

arXiv2026

On Perturbatively Dressed Observables

A central lesson of gravity is that local observables are ill-defined. Coordinates themselves are a redundancy of description, so any particular point in spacetime is only meaningful once defined relationally by clocks, rulers, or asymptotic data. Despite extensive formal work on this subject, explicit calculations of the resulting gravitationally-dressed observables are more scarce. In this paper we perturbatively compute dressed matrix elements of local operators in electrodynamics and general relativity, including both potential and radiative photons and gravitons. Our expressions indicate that dressing is not ornamental: it universally induces kinematic singularities that can substantively reshape observables. We further show how dressing is mathematically equivalent to gauge fixing, as demonstrated by a dynamical temporal gauge in which the gauge-fixing vector is itself a geodesic fluid.

hep-th↗

arXiv2025

Conservative Dynamics of Relativistic Binaries Beyond Einstein Gravity

We study the conservative dynamics of spinless compact objects in a general effective theory of gravity which includes a metric and an arbitrary number of scalar fields, through $\mathcal{O}(G^{3})$. Departures from Einstein gravity, which preserve general coordinate and local Lorentz invariance, are characterized by higher-derivative terms in a Lagrangian whose coupling constants scale as powers of a ``new-physics'' length scale, $\ell$. For a purely metric theory we compute the contributions from the the leading and subleading higher-curvature curvature corrections. In four dimensions these are cubic and quartic curvature terms, i.e. orders $\ell^4$ and $\ell^6$. We also study a general multi-scalar-tensor theory of gravity to order $\ell^{4}$, which includes both Einstein-dilaton-Gauss-Bonnet (EdGB) and dynamical Chern-Simons (dCS) higher-order couplings. Specifically, we compute the radial action in a post-Minkowskian approximation for scattering orbits, to two-loop order. The result encodes the fully relativistic dynamics of the compact objects, and serves as a generating function for gauge-invariant orbital observables for both bound and unbound binary systems. Where overlapping post-Newtonian results are available, we've verified agreement.

hep-th↗

arXiv2024

On the Motion of Compact Objects in Relativistic Viscous Fluids

We present a world-line effective field theory of compact objects moving relativistically through a viscous fluid. The theory is valid when velocity gradients are small compared to the inverse size of the object. Working within the EFT eliminates the need to solve a boundary value problem by turning all interactions between the fluid and the object into a source term in the action. We use the EFT to derive the relativistic equations of motion for a compact object immersed in a viscous fluid in a curved background.

gr-qc↗

arXiv2024

Gravitational Scattering and Beyond from Extreme Mass Ratio Effective Field Theory

We explore a recently proposed effective field theory describing electromagnetically or gravitationally interacting massive particles in an expansion about their mass ratio, also known as the self-force (SF) expansion. By integrating out the deviation of the heavy particle about its inertial trajectory, we obtain an effective action whose only degrees of freedom are the lighter particle together with the photon or graviton, all propagating in a Coulomb or Schwarzschild background. The 0SF dynamics are described by the usual background field method, which at 1SF is supplemented by a "recoil operator" that encodes the wobble of the heavy particle, and similarly computable corrections appearing at 2SF and higher. Our formalism exploits the fact that the analytic expressions for classical backgrounds and particle trajectories encode dynamical information to all orders in the couplings, and from them we extract multiloop integrands for perturbative scattering. As a check, we study the two-loop classical scattering of scalar particles in electromagnetism and gravity, verifying known results. We then present new calculations for the two-loop classical scattering of dyons, and of particles interacting with an additional scalar or vector field coupling directly to the lighter particle but only gravitationally to the heavier particle.

hep-th↗

arXiv2024

Decoherence by warm horizons

Recently Danielson, Satishchandran, and Wald (DSW) have shown that quantum superpositions held outside of Killing horizons will decohere at a steady rate. This occurs because of the inevitable radiation of soft photons (gravitons), which imprint a electromagnetic (gravitational) ``which-path'' memory onto the horizon. Rather than appealing to this global description, an experimenter ought to also have a local description for the cause of decoherence. One might intuitively guess that this is just the bombardment of Hawking/Unruh radiation on the system, however simple calculations challenge this idea -- the same superposition held in a finite temperature inertial laboratory does not decohere at the DSW rate. In this work we provide a local description of the decoherence by mapping the DSW set-up onto a worldline-localized model resembling an Unruh-DeWitt particle detector. We present an interpretation in terms of random local forces which do not sufficiently self-average over long times. Using the Rindler horizon as a concrete example we clarify the crucial role of temperature, and show that the Unruh effect is the only quantum mechanical effect underlying these random forces. A general lesson is that for an environment which induces Ohmic friction on the central system (as one gets from the classical Abraham-Lorentz-Dirac force, in an accelerating frame) the fluctuation-dissipation theorem implies that when this environment is at finite temperature it will cause steady decoherence on the central system. Our results agree with DSW and provide the complementary local perspective.

hep-th↗

arXiv2023

Testing Quantum Gravity using Pulsed Optomechanical Systems

An interesting idea, dating back to Feynman, argues that quantum mechanics may break down for large masses if one entertains the possibility that gravity can be "classical", thereby leading to predictions different from conventional low-energy quantum gravity. Despite the technical difficulty in testing such deviations, a large number of experimental proposals have been put forward due to the high level of fundamental interest. Here, we consider the Schr\"odinger-Newton (SN) theory and the Correlated Worldline (CWL) theory, and show that they can be distinguished from conventional quantum mechanics, as well as each other, by performing pulsed optomechanics experiments. For CWL specifically we develop a framework resembling the commonly used "Heisenberg-picture" treatment of coupled oscillators, allowing one to perform simple calculations for such systems without delving into the deeper path-integral formalism. We find that discriminating between the theories will be very difficult until experimental control over low frequency quantum optomechanical systems is pushed much further. However, the predicted departures of SN and CWL from quantum mechanics occur at the same scale, so both alternative models could in principle be probed by a single experiment.

quant-ph↗

arXiv2023

Conservative Scattering of Reissner-Nordstr\"om Black Holes at Third Post-Minkowskian Order

Using a recently developed effective field theory formalism for extreme mass ratios [2308.14832], we present a calculation of charged black hole scattering at third post-Minkowskian order. The charges and masses are kept arbitrary, and the result interpolates from the scattering of Schwarzschild to extremal charged black holes, and beyond to charged particles in electrodynamics -- agreeing with previously reported results in all such limits. The computation of the radial action is neatly organized in powers of the mass ratio. The probe (0SF) contributions are readily computed by direct integration of the radial momentum, and we use the effective field theory to compute the subleading (1SF) contributions via background-field Feynman rules supplemented by an operator encoding recoil of the background. Together these contributions completely determine the conservative physics at order~$\mathcal{O}(G^{3})$.

hep-th↗

arXiv2023

Effective Field Theory for Extreme Mass Ratios

We derive an effective field theory describing a pair of gravitationally interacting point particles in an expansion in their mass ratio, also known as the self-force (SF) expansion. The 0SF dynamics are trivially obtained to all orders in Newton's constant by the geodesic motion of the light body in a Schwarzschild background encoding the gravitational field of the heavy body. The corrections at 1SF and higher are generated by perturbations about this configuration -- that is, the geodesic deviation of the light body and the fluctuation graviton -- but crucially supplemented by an operator describing the recoil of the heavy body as it interacts with the smaller companion. Using this formalism we compute new results at third post-Minkowskian order for the conservative dynamics of a system of gravitationally interacting massive particles coupled to a set of additional scalar and vector fields.

hep-th↗

arXiv2022

Propagators in the Correlated Worldline Theory of Quantum Gravity

Starting from a formulation of Correlated Worldline (CWL) theory in terms of functional integrals over paths, we define propagators for particles and matter fields in this theory. We show that the most natural formulation of CWL theory involves a rescaling of the generating functional for the theory; correlation functions then simplify, and all loops containing gravitons disappear from perturbative expansions. The spacetime metric obeys the Einstein equation, sourced by all of the interacting CWL paths. The matter paths are correlated by gravitation, thereby violating quantum mechanics for large masses. We derive exact results for the generating functional and the matter propagator, and for linearized weak field theory. For the example of a two-path experiment, we derive the CWL matter propagator, and show how the results compare with conventional quantum theory and with semiclassical gravity. We also exhibit the structure of low-order perturbation theory for the CWL matter propagator.

gr-qc↗

arXiv2021

Soft Theorems from Boundary Terms in the Classical Point Particle Currents

Soft factorization has been shown to hold to sub-leading order in QED and to sub-sub-leading order in perturbative quantum gravity, with various loop and non-universal corrections that can be found. Here we show that all terms factorizing at tree level can be uniquely identified as boundary terms that exist already in the classical expressions for the electric current and stress tensor of a point particle. Further, we show that one cannot uniquely identify such boundary terms beyond the sub-leading or sub-sub-leading orders respectively, providing evidence that the "universality" of the tree level soft factor only holds to these orders. Finally, we show that these boundary terms factor out of all tree level amplitudes as expected, in a theory where gravitons couple to a scalar field.

hep-th↗

arXiv2020

Yang-Mills Gauss law and the heavy quark binding energy in the presence of a dimension-2 gluon condensate

We study the binding energy of a heavy quark-antiquark ($q\bar{q}$) pair using the first-order path integral formalism. This makes the Yang-Mills constraint equation explicit, and highlights that it is valid without relying on a semiclassical approximation. A generalized gauge-covariant Coulomb gauge is chosen to allow for a decomposition of the chromoelectric field into a gauge-covariant generalization of transverse and longitudinal parts. This decomposition makes it clear that the $q\bar{q}$ binding energy is determined solely by the solution to the constraint equation. Assuming that the low-energy physics is dominated by the existence of a dimension-2 gluon condensate, we develop an asymptotic series solution to the constraint equation and thus to the $q\bar{q}$ binding energy. We predict a QCD string tension in terms of the condensate strength and quadratic Casimir eigenvalues, and relate our result to results coming from OPE analyses.

hep-ph↗

arXiv2020

Gauge Invariant Propagators and States in Quantum Electrodynamics

We study gauge invariant states in QED, where states are understood in terms of data living on the boundary of gauge invariant path-integrals. This is done for both scalar and spinor QED, and for boundaries that are either time slices, or the boundaries of a 'causal diamond'. We discuss both the case where the gauge field falls off to zero at the boundaries, and the case of 'large gauge transformations', where it remains finite at the boundaries. The dynamics are discussed using the gauge-invariant propagator, describing motion of both the particles and the field between the boundaries. We demonstrate how the path-integral naturally generates a 'Coulomb-field' dressing factor for states living on time-slices, and how this is done without fixing any gauge. We show that the form of the dressing depends only on the nature of the boundaries. We also derive the analogous dressing for states defined on null infinity, showing both its Coulombic parts as well as soft-photon parts.

hep-th↗

arXiv2019

Gravitational Decoherence, Asymptotic Quantization, and Entanglement Measures

Graviton emission decoheres superpositions of matter states. We write the decoherence rate in terms of a "differential Bondi news" function, and show that this function can be written as an overlap integral between different asymptotic radiative states given by Ashtekar. This result - while derived in the linearized theory - is ultimately expressed for asymptotically flat space-times in terms of variables with unambiguous geometric meaning in the full theory. We treat a simple two-path experiment, and compute the differential news, the purity, the entanglement entropy, and the fidelity, to make explicit the connection with the information loss.

gr-qc↗

arXiv2018

A functional approach to soft graviton scattering and BMS charges

We consider the interaction between a matter system and soft gravitons. We use a functional eikonal expansion to deal with the infrared divergences, and introduce a "composite generating functional" which allows us to calculate a decoherence functional for the time evolution of the system. These techniques allow us to formulate scattering problems in a way which deals consistently with infrared effects, as well as being manifestly diffeomorphism invariant. We show how the asymptotic form of the decoherence functional can be written in terms of the infinitely many conserved charges associated with asymptotic BMS symmetries, and allow us to address the question of how much information is lost during the scattering.

gr-qc↗

arXiv2015

Black hole energy extraction via stationary scalar clouds

We study scalar field configurations around Kerr black holes with a time-independent energy-momentum tensor. These stationary `scalar clouds', confined near the black hole (BH) by their own mass or a mirror at fixed radius, exist at the threshold for energy extraction via superradiance. Motivated by the electromagnetic Blandford-Znajek (BZ) mechanism, we explore whether scalar clouds could serve as a proxy for the force-free magnetosphere in the BZ process. We find that a stationary energy-extracting scalar cloud solution exists when the reflecting mirror is replaced by a semi-permeable surface which allows the cloud to radiate some energy to infinity while maintaining self-sustained superradiance. The radial energy flux displays the same behaviour for rapidly rotating holes as magnetohydrodynamic simulations predict for the BZ mechanism.

hep-th↗