World Lines Of Particles Research Articles

A symmetry principle for gauge theories with fractons

Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose conserved charges do not commute with spatial translations. We refer to such symmetries as nonuniform higher-form symmetries. These symmetries fall within the standard definition of higher-form symmetries in quantum field theory, and the corresponding symmetry generators are topological. Worldlines of particles are regarded as the charged objects of 1-form symmetries, and mobility restrictions can be implemented by introducing additional 1-form symmetries whose generators do not commute with spatial translations. These features are realized by effective field theories associated with spontaneously broken nonuniform 1-form symmetries. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu-Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. The gauge theories have emergent nonuniform magnetic symmetries, and some of the magnetic monopoles become fractonic. We identify the ’t Hooft anomalies of the nonuniform higher-form symmetries and the corresponding bulk symmetry-protected topological phases. By this method, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions.

The galaxy power spectrum on the lightcone: deep, wide-angle redshift surveys and the turnover scale

We derive expressions for the survey-window convolved galaxy power spectrum in real space for a full sky and deep redshift survey, but taking into account the geometrical lightcone effect. We investigate the impact of using the standard mean redshift approximation as a function of survey depth, and show that this assumption can lead to both an overall amplitude suppression and scale-dependent error when compared to the 'true' spectrum. However, we also show that by using a carefully chosen 'effective fixed-time', one can find a range of scales where the approximation to the full model is highly accurate, but only on a more restricted set of scales. We validate the theory by constructing dark matter and galaxy lightcone mock surveys from a large N-body simulation with a high cadence of snapshots. We do this by solving the light cone equation exactly for every particle, where the particle worldlines are obtained in a piecewise fashion with cubic interpolation between neighbouring snapshots. We find excellent agreement between our measurements and the theory (∼ ±5%) over scales (0.004 h Mpc-1 ≤ k ≤ 0.54 h Mpc-1) and for a variety of magnitude limits. Finally, we look to see how accurately we can measure the turnover scale of the galaxy power spectrum k 0. Using the lightcone mocks we show that one can detect the turnover scale with a probability P ≥ 95% in an all-sky catalogue limited to an apparent magnitude m lim ∼ 21. We also show that the detection significance would remain high for surveys with m lim ∼ 22 and 20% sky coverage.

Duality and singularities of world sheets and worldlines of geometric particles along framed base curves in world hyper-sheet

In this paper, as applications of singularity theory, we consider the singularities of a world sheet and the traveling trajectory (i.e. a worldline) of a geometric particle when they are confined in a world hyper-sheet and are generated by a Sabban framed base curve in de Sitter 3-space. Using the approach of the unfolding theory in singularity theory, we establish the relationships between the world sheet, the worldline of the geometric particle and two invariants to characterize the local topological structures of singularities of the world sheet and the worldline of the geometric particle via these two invariants, respectively. Moreover, we also describe the dual relationships between the tangent curve of framed base curve and the worldline of the geometric particle. An important fact indicates that the worldline [Formula: see text] and the tangent curve [Formula: see text] of the original curve [Formula: see text] are [Formula: see text]-dual each other. Finally, two concrete examples are presented to interpret our theoretical results.

Particles in the superworldline and BRST

In this short note we discuss $N$-supersymmetric worldlines of relativistic massless particles and review the known result that physical spin-$N/2$ fields are in the first BRST cohomology group. For $N=1,2,4$, emphasis is given to particular deformations of the BRST differential, that implement either a covariant derivative for a gauge theory or a metric connection in the target space seen by the particle. In the end, we comment about the possibility of incorporating Ramond-Ramond fluxes in the background.

An application of symplectic integration for general relativistic planetary orbitography subject to non-gravitational forces

Spacecraft propagation tools describe the motion of near-Earth objects and interplanetary probes using Newton’s theory of gravity supplemented with the approximate general relativistic n-body Einstein–Infeld–Hoffmann equations of motion. With respect to the general theory of relativity and the long-standing recommendations of the International Astronomical Union for astrometry, celestial mechanics and metrology, we believe modern orbitography software is now reaching its limits in terms of complexity. In this paper, we present the first results of a prototype software titled General Relativistic Accelerometer-based Propagation Environment (GRAPE). We describe the motion of interplanetary probes and spacecraft using extended general relativistic equations of motion which account for non-gravitational forces using end-user supplied accelerometer data or approximate dynamical models. We exploit the unique general relativistic quadratic invariant associated with the orthogonality between four-velocity and acceleration and simulate the perturbed orbits for Molniya, Parker Solar Probe and Mercury Planetary Orbiter-like test particles subject to a radiation-like four-force. The accuracy of the numerical procedure is maintained using a 5-stage, 10^mathrm{th}-order structure-preserving Gauss collocation symplectic integration scheme. GRAPE preserves the norm of the tangent vector to the test particle worldline at the order of 10^{-32}.

Holographic entanglement entropy in AdS3/WCFT

In this paper, we consider AdS3 with Compère-Song-Strominger (CSS) boundary conditions, under which the dual field theory is warped conformal field theory (WCFT), featuring a Virasoro-Kac-Moody algebra. We provide a holographic dual picture of the single interval entanglement entropy in WCFT in the bulk AdS3. We explicitly show that the bulk object captures the entanglement entropy in WCFT is a massive spinning particle's worldline that anchored on the boundary of the interval. Given the mass and spin of the particle as functions of quantum numbers of the twist operator in WCFT, the on-shell worldline action will match the entanglement entropy in WCFT.

EFT approach to general relativity: correction to EIH Lagrangian due to electromagnetic charge

We extend the Non-Relativistic formulation of General Relativity (NRGR) given in Goldberger et al. (Phys Rev D 73:104029, 2006) to incorporate the effects of electromagnetic charge of the constituents of the binary. We incorporate the photon field in NRGR by giving the field decomposition and power counting rules. Using these, we develop the Feynman rules to describe photon and graviton interactions with point particle worldline. We then find the corrections to the Einstein-Infeld-Hoffmann Lagrangian (Einstein et al. in Ann Math 39:65-100, 1938) due to the presence of the photon field and electromagnetic charge of the constituents of the binary.

Colloquium : Bell’s theorem and locally mediated reformulations of quantum mechanics

Bell's Theorem rules out many potential reformulations of quantum mechanics, but within a generalized framework, it does not exclude all "locally-mediated" models. Such models describe the correlations between entangled particles as mediated by intermediate parameters which track the particle world-lines and respect Lorentz covariance. These locally-mediated models require the relaxation of an arrow-of-time assumption which is typically taken for granted. Specifically, some of the mediating parameters in these models must functionally depend on measurement settings in their future, i.e., on input parameters associated with later times. This option (often called "retrocausal") has been repeatedly pointed out in the literature, but the exploration of explicit locally-mediated toy-models capable of describing specific entanglement phenomena has begun only in the past decade. A brief survey of such models is included here. These models provide a continuous and consistent description of events associated with spacetime locations, with aspects that are solved "all-at-once" rather than unfolding from the past to the future. The tension between quantum mechanics and relativity which is usually associated with Bell's Theorem does not occur here. Unlike conventional quantum models, the number of parameters needed to specify the state of a system does not grow exponentially with the number of entangled particles. The promise of generalizing such models to account for all quantum phenomena is identified as a grand challenge.

An exact quantization of Jackiw-Teitelboim gravity

We propose an exact quantization of two-dimensional Jackiw-Teitelboim (JT) gravity by formulating the JT gravity theory as a 2D gauge theory placed in the presence of a loop defect. The gauge group is a certain central extension of PSL(2, ℝ) by ℝ. We find that the exact partition function of our theory when placed on a Euclidean disk matches precisely the finite temperature partition function of the Schwarzian theory. We show that observables on both sides are also precisely matched: correlation functions of boundary- anchored Wilson lines in the bulk are given by those of bi-local operators in the Schwarzian theory. In the gravitational context, the Wilson lines are shown to be equivalent to the world-lines of massive particles in the metric formulation of JT gravity.

Quantum harmonic oscillator, entanglement in the vacuum and its geometric interpretation

Inspired by ER=EPR conjecture we present a mathematical tool providing a link between quantum entanglement and the geometry of spacetime. We start with the idea of operators in extended Hilbert space which, by definition, has no positive definite scalar product. Adopting several simple postulates we show that a quantum harmonic oscillator can be constructed as a positive definite sector in that space. We discuss the two-dimensional oscillator constructed in such a way that the ground state is maximally entangled. Being a vector in the Hilbert space, it has also a non-trivial expansion in a bigger extended space. On one hand, the space is not free of negative norm states. On the other hand, it allows one to interpret the ground state geometrically in terms of AdS3. The interpretation is based solely on the form of the expansion, revealing certain structures at the boundary and in the bulk of AdS3. The former corresponds to world lines of massless particles at the boundary. The latter resembles interacting closed strings.

A Frenet–Serret interpretation of particle dynamics in high-intensity laser fields

In this paper we discuss the dynamics of charged particles in high-intensity laser fields in the context of the Frenet–Serret formalism, which describes the intrinsic geometry of particle world lines. We find approximate relations for the Frenet–Serret scalars and basis vectors relevant for high-intensity laser particle interactions. The onset of quantum effects relates to the curvature radius of classical trajectories being on the order of the Compton wavelength. The effects of classical radiation reaction are discussed, as well as the classical precession of the spin-polarization vector according to the Thomas–Bargman–Michel–Telegdi equation. We comment on the derivation of the photon emission rate in strong-field QED beyond the locally constant field approximation, which is used in Monte Carlo simulations of quantum radiation reaction. Such a numerical simulation is presented for a possible experiment to distinguish between classical and quantum mechanical models of radiation reaction.

Properties of the innermost stable circular orbit of a spinning particle moving in a rotating Maxwell-dilaton black hole background

In this paper we investigate the innermost stable circular orbit (ISCO) of a spinning test particle moving in the rotating Maxwell-dilaton black hole spacetime. By using the Mathisson-Papapetrou-Dixon equations along with the Tulczyjew spin-supplementary condition, we find the equations of motion in the equatorial plane and, from the radial equation, it is obtained the effective potential for the description of the particle's motion. The obtained trajectories show that the ISCO radii for spinning particles moving in rotating charged backgrounds are always smaller than those obtained in the corresponding Kerr-Newman spacetimes. The increasing in the particle's spin produces a decrease in the ISCO radius in all the studied cases, with a maximum value for the spin and a corresponding minimum ISCO radius, obtained by imposing a condition that guarantees the timelike nature of the particle's worldline.

Theory of metaparticles

We introduce and develop the theory of metaparticles. At the classical level, this is a world-line theory with the usual reparameterization invariance and two additional features. The theory is motivated by string theory on compact targets, and can be thought of, at least at the non-interacting level, as a theory of particles at a given string level, or as a particle model for Born geometries. The first additional feature of the model is the presence of an additional local symmetry, which from the string point of view corresponds to the completion of worldsheet diffeomorphism invariance. From the particle world-line point of view, this symmetry is associated with an additional local constraint. The second feature is the presence of a non-trivial symplectic form on the metaparticle phase space, also motivated by string theory [1, 2]. Because of its interpretation as a particle model on Born geometry, the space-time on which the metaparticle propagates is ambiguous, with different choices related by what in string theory we would call T-duality. In this paper, we define the model, and explore some of its principle classical and quantum properties, including causality and unitarity.

Chiral anomaly, Berry phase, and chiral kinetic theory from worldlines in quantum field theory

We outline a novel chiral kinetic theory framework for systematic computations of the Chiral Magnetic Effect (CME) in ultrarelativistic heavy-ion collisions. The real part of the fermion determinant in the QCD effective action is expressed as a supersymmetric world-line action of spinning, colored, Grassmanian point particles in background gauge fields, with equations of motion that are covariant generalizations of the Bargmann-Michel-Telegdi and Wong equations. Berry's phase is obtained in a consistent non-relativistic adiabatic limit. The chiral anomaly, in contrast, arises from the phase of the fermion determinant; its topological properties are therefore distinct from those of the Berry phase. We show that the imaginary contribution to the fermion determinant too can be expressed as a point particle world-line path integral and derive the corresponding anomalous axial vector current. Our results can be used to derive a covariant relativistic chiral kinetic theory including the effects of topological fluctuations that has overlap with classical-statistical simulations of the CME at early times and anomalous hydrodynamics at late times.

World sheets of spinning particles

The classical spinning particles are considered such that quantization of classical model leads to an irreducible massive representation of the Poincar\'e group. The class of gauge equivalent classical particle world lines is shown to form a $[(d+1)/2]$-dimensional world sheet in $d$-dimensional Minkowski space, irrespectively to any specifics of classical model. For massive spinning particles in $d=3,4$, the world sheets are shown to be cylinders. The radius of cylinder is fixed by representation. In higher dimensions, particle's world sheet turn out to be a toroidal cylinder $\mathbb{R}\times \mathbb{T}^D$, $D=[(d-1)/2]$. Proceeding from the fact that the world lines of irreducible classical spinning particles are cylindrical curves, while all the lines are gauge equivalent on the same world sheet, we suggest a method to deduce the classical equations of motion for particles and also to find their gauge symmetries. In $d=3$ Minkowski space, the spinning particle path is defined by a single fourth-order differential equation having two zero-order gauge symmetries. The equation defines particle's path in Minkowski space, and it does not involve auxiliary variables. A special case is also considered of cylindric null-curves, which are defined by a different system of equations. It is shown that the cylindric null-curves also correspond to irreducible massive spinning particles. For the higher-derivative equation of motion of the irreducible massive spinning particle, we deduce the equivalent second-order formulation involving an auxiliary variable. The second-order formulation agrees with a previously known spinning particle model.

Deviation and precession effects in the field of a weak gravitational wave

Deviation and precession effects of a bunch of spinning particles in the field of a weak gravitational plane wave are studied according to the Mathisson-Papapetrou-Dixon (MPD) model. Before the passage of the wave the particles are at rest with associated spin vector aligned along a given direction with constant magnitude. The interaction with the gravitational wave causes the particles to keep moving on the 2-plane orthogonal to the direction of propagation of the wave, with the transverse spin vector undergoing oscillations around the initial orientation. The transport equations for both the deviation vector an spin vector between two neighboring world lines of such a congruence are then solved by a suitable extension of the MPD model off the spinning particle's world line. In order obtain measurable physical quantities a "laboratory" has been set up by constructing a Fermi coordinate system attached to a reference world line. The {\it exact} transformation between TT coordinates and Fermi coordinates is derived too.

Speeds of light in Stueckelberg-Horwitz-Piron electrodynamics

Stueckelberg-Horwitz-Piron (SHP) electrodynamics formalizes the distinction between coordinate time (measured by laboratory clocks) and chronology (temporal ordering) by defining 4D spacetime events xμ as functions of an external evolution parameter τ. As τ grows monotonically, the spacetime evolution of classical events xμ (τ) trace out particle worldlines dynamically and induce the five U(1) gauge potentials through which events interact.In analogy with the constant c that associates a unit of length x0 with intervals of time t in standard relativity, we introduce a constant c5 associated with the external time τ. Whereas the nonrelativistic limit of special relativity can be found by taking c → ∞, we show that 5D SHP goes over to an equilibrium state of Maxwell theory in the limit c5 → 0. Thus, the dimensionless ratio c5/c parameterizes the deviation of SHP from standard electrodynamics, in particular the coupling of events. Put another way, Maxwell theory can be understood as currents and fields relaxing to an equilibrium independent of chronological time as c5τ slows to zero. We find that taking 0 < c5/c < 1 enables the resolution of several longstanding difficulties in SHP theory.

Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime

If a small "particle" of mass $\mu M$ (with $\mu \ll 1$) orbits a black hole of mass $M$, the leading-order radiation-reaction effect is an $\mathcal{O}(\mu^2)$ "self-force" acting on the particle, with a corresponding $\mathcal{O}(\mu)$ "self-acceleration" of the particle away from a geodesic. Such "extreme--mass-ratio inspiral" systems are likely to be important gravitational-wave sources for future space-based gravitational-wave detectors. Here we consider the "toy model" problem of computing the self-force for a scalar-field particle on a bound eccentric orbit in Kerr spacetime. We use the Barack-Golbourn-Vega-Detweiler effective-source regularization with a 4th order puncture field, followed by an $e^{im\phi}$ ("m-mode") Fourier decomposition and a separate time-domain numerical evolution in $2+1$ dimensions for each $m$. We introduce a finite worldtube that surrounds the particle worldline and define our evolution equations in a piecewise manner so that the effective source is only used within the worldtube. Viewed as a spatial region, the worldtube moves to follow the particle's orbital motion. We use slices of constant Boyer-Lindquist time in the region of the particle's motion, deformed to be asymptotically hyperboloidal and compactified near the horizon and $\mathcal{J}^+$. We present numerical results for a number of test cases with orbital eccentricities as high as $0.98$. In some cases we find large oscillations ("wiggles") in the self-force shortly after periastron passage.

Multi-centered AdS3 solutions from Virasoro conformal blocks

We revisit the construction of multi-centered solutions in three-dimensional anti-de Sitter gravity in the light of the recently discovered connection between particle worldlines and classical Virasoro conformal blocks. We focus on multi-centered solutions which represent the backreaction of point masses moving on helical geodesics in global AdS3, and argue that their construction reduces to a problem in Liouville theory on the disk with Zamolodchikov-Zamolodchikov boundary condition. In order to construct the solution one needs to solve a certain monodromy problem which we argue is solved by a vacuum classical conformal block on the sphere in a particular channel. In this way we construct multi-centered gravity solutions by using conformal blocks special functions. We show that our solutions represent left-right asymmetric configurations of operator insertions in the dual CFT. We also provide a check of our arguments in an example and comment on other types of solutions.

Gauged twistor formulation of a massive spinning particle in four dimensions

We present a gauged twistor model of a free massive spinning particle in four-dimensional Minkowski space. This model is governed by an action, referred to here as the gauged generalized Shirafuji (GGS) action, that consists of twistor variables, auxiliary variables, and $U(1)$ and $SU(2)$ gauge fields on the one-dimensional parameter space of a particle's worldline. The GGS action remains invariant under reparametrization and the local $U(1)$ and $SU(2)$ transformations of the relevant variables, although the $SU(2)$ symmetry is nonlinearly realized. We consider the canonical Hamiltonian formalism based on the GGS action in the unitary gauge by following Dirac's recipe for constrained Hamiltonian systems. It is shown that just sufficient constraints for the twistor variables are consistently derived by virtue of the gauge symmetries of the GGS action. In the subsequent quantization procedure, these constraints turn into simultaneous differential equations for a twistor function. We perform the Penrose transform of this twistor function to define a massive spinor field of arbitrary rank, demonstrating that the spinor field satisfies generalized Dirac-Fierz-Pauli equations with $SU(2)$ indices. We also investigate the rank-one spinor fields in detail to clarify the physical meanings of the $U(1)$ and $SU(2)$ symmetries.