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P. A. Horvathy

Publications and source records attributed to P. A. Horvathy.

At least 37 records · Page 2Linked to original sources
arXiv2025

A generalized Noether theorem for scaling symmetry

The recently discovered conserved quantity associated with Kepler rescaling is generalised by an extension of Noether's theorem which involves the classical action integral as an additional term. For a free particle the familiar Schroedinger dilations are recovered. A general pattern arises for homogeneous potentials. The associated conserved quantity allows us to derive the virial theorem. The relation to the Bargmann framework is explained and illustrated by exact plane gravitational waves.

math-ph↗
arXiv2025

Lukash plane waves, revisited

The Lukash metric is a homogeneous gravitational wave which at late times approximates the behaviour of a generic class of spatially homogenous cosmological models with monotonically decreasing energy density. The transcription from Brinkmann to Baldwin-Jeffery-Rosen (BJR) to Bianchi coordinates is presented and the relation to a Sturm-Liouville equation is explained. The 6-parameter isometry group is derived. In the Bianchi VII range of parameters we have two BJR transciptions. However using either of them induces a mere relabeling of the geodesics and isometries. Following pioneering work of Siklos, we provide a self-contained account of the geometry and global structure of the spacetime. The latter contains a Killing horizon to the future of which the spacetime resembles an anisotropic version of the Milne cosmology and to the past of which it resemble the Rindler wedge.

gr-qc↗
arXiv2025

Peierls substitution and Hall motion in exotic Carroll dynamics

The particle with first-order dynamics proposed by Dunne, Jackiw and Trugenberger (DJT) to justify the ``Peierls substitution" is obtained by reduction from both of the planar two-parameter centrally extended Galilean and Carroll systems. In the latter case the extension parameters $κ_{exo}$ and $κ_{mag}$ generate non-commutativity of the coordinates resp. behave as an internal magnetic field. The position and momentum follow uncoupled anomalous Hall motions. Consistently with partial immobility, one of the Carroll boost generators is broken but the other remains a symmetry. Switching off $κ_{exo}$, the immobility of unextended Carroll particles is recovered. The Carroll system is dual to an uncharged anyon on the horizon of a black hole which exhibits the spin-Hall effect. Physical applications are shortly reviewed.

hep-th↗
arXiv2025

Gravitational wave memory: further examples

Ehlers and Kundt [1] argued in favor of the velocity effect: particles initally at rest hit by a burst of gravitational waves should fly apart with constant velocity after the wave has passed. Zel'dovich and Polnarev [2] suggested instead that waves generated by flyby would be merely displaced. Their prediction is confirmed provided the wave parameters take some particular values.

gr-qc↗
arXiv2025

MultiCarroll dynamics

Unlike a single Carroll particle, a multiparticle Carroll system can move under suitable conditions, as we demonstrate it explicitly for two particles with a momentum-dependent interaction: the center-of-mass remains fixed, however relative motion is possible, confirming previous statements made by Bergshoeff, Casalbuoni, and their collaborators. Analogous results are obtained for electric dipoles with the roles of the center-of-mass and the relative position interchanged.

gr-qc↗
arXiv2025

Displacement within velocity effect in gravitational wave memory

Particles initially at rest hit by a passing sandwich gravitational wave exhibit, in general, thevelocity memory effect (VM): they fly apart with constant velocity. For specific values of the wave parameters their motion can however become pure displacement (DM) as suggested by Zel'dovich and Polnarev. For such a ``miraculous'' value, the particle trajectory is composed of an integer number of (approximate) standing half-waves. Our statements are illustrated numerically by a Gaussian, and analytically by the Pöschl-Teller profiles.

gr-qc↗
arXiv2018

Velocity Memory Effect for Polarized Gravitational Waves

Circularly polarized gravitational sandwich waves exhibit, as do their linearly polarized counterparts, the Velocity Memory Effect: freely falling test particles in the flat after-zone fly apart along straight lines with constant velocity. In the inside zone their trajectories combine oscillatory and rotational motions in a complicated way. For circularly polarized periodic gravitational waves some trajectories remain bounded, while others spiral outward. These waves admit an additional "screw" isometry beyond the usual five. The consequences of this extra symmetry are explored.

gr-qc↗
arXiv2018

Cosmological aspects of the Eisenhart-Duval lift

A cosmological extension of the Eisenhart-Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed the Ermakov-Milne-Pinney equation. Killing isometries include spatial translations and rotations, Newton--Hooke boosts and translation in the null direction. Geodesic motion in Ermakov-Milne-Pinney cosmoi is analyzed. The derivation of the Ermakov-Lewis invariant, the Friedmann equations and the Dmitriev-Zel'dovich equations within the Eisenhart--Duval framework is presented.

gr-qc↗
arXiv2018

Memory Effect for Impulsive Gravitational Waves

Impulsive gravitational plane waves, which have a delta-function singularity on a hypersurface, can be obtained by squeezing smooth plane gravitational waves with Gaussian profile. They exhibit (as do their smooth counterparts) the Velocity Memory Effect: after the wave has passed, particles initially at rest move apart with non vanishing constant transverse velocity. A new effect is that, unlike to the smooth case, (i) the velocities of particles originally at rest jump, (ii) the spacetime trajectories become discontinuous along the (lightlike) propagation direction of the wave.

gr-qc↗
arXiv2017

Soft Gravitons & the Memory Effect for Plane Gravitational Waves

The "gravitational memory effect" due to an exact plane wave provides us with an elementary description of the diffeomorphisms associated with soft gravitons. It is explained how the presence of the latter may be detected by observing the motion of freely falling particles or other forms of gravitational wave detection. Numerical calculations confirm the relevance of the first, second and third time integrals of the Riemann tensor pointed out earlier. Solutions for various profiles are constructed. It is also shown how to extend our treatment to Einstein-Maxwell plane waves and a midi-superspace quantization is given.

gr-qc↗
arXiv2017

The Memory Effect for Plane Gravitational Waves

We give an account of the gravitational memory effect in the presence of the exact plane wave solution of Einstein's vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles. The theorem of Bondi and Pirani on caustics (for which we present a new proof) implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zel'dovich and Polnarev. A non-vanishing asymptotic relative velocity might be used to detect gravitational waves through the "velocity memory effect", considered by Braginsky, Thorne, Grishchuk, and Polnarev.

gr-qc↗
arXiv2017

Carroll symmetry of plane gravitational waves

The well-known 5-parameter isometry group of plane gravitational waves in $4$ dimensions is identified as Levy-Leblond's Carroll group in $2+1$ dimensions with no rotations. Our clue is that plane waves are Bargmann spaces into which Carroll manifolds can be embedded. We also comment on the scattering of light by a gravitational wave and calculate its electric permittivity considered as an impedance-matched metamaterial.

gr-qc↗
arXiv2017

Duality and helicity: the photon wave function approach

The photon wave equation proposed in terms of the Riemann-Silberstein vector is derived from a first-order Dirac/Weyl-type action principle. It is symmetric w.r.t. duality transformations, but the associated Noether quantity vanishes. Replacing the fields by potentials and using instead a quadratic Klein-Gordon-type Lagrangian allows us to recover the double-Chern-Simons expression of conserved helicity and is shown to be equivalent to recently proposed alternative frameworks. Applied to the potential-modified theory the Dirac/Weyl-type approach yields again zero conserved charge, whereas the Klein-Gordon-type approach applied to the original setting yields Lipkin's "zilch".

hep-th↗
arXiv2016

Duality and helicity: a symplectic viewpoint

The theorem which says that helicity is the conserved quantity associated with the duality symmetry of the vacuum Maxwell equations is proved by viewing electromagnetism as an infinite dimensional symplectic system. In fact, it is shown that helicity is the moment map of duality acting as an $SO(2)$ group of canonical transformations on the symplectic space of all solutions of the vacuum Maxwell equations.

math-ph↗
arXiv2016

Eisenhart lifts and symmetries of time-dependent systems

Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with $n$ degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann spacetime in $n+2$ dimensions, equipped with its covariantly constant null Killing vector field. Reparametrization of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola-Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schrödinger equation emerges naturally using the techniques of quantum field theory in curved spacetimes, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space. Time-dependent Lagrangians arise naturally also in cosmology and give rise to the phenomenon of Hubble friction. We provide an account of this for Friedmann-Lemaitre and Bianchi cosmologies and how it fits in with our previous discussion in the non-relativistic limit.

hep-th↗
arXiv2016

Helicity of spin-extended chiral particles

The helicity of a free massless relativistic particle, $χ^o={\bf s}.{\bf p}/|{\bf p}|$, is generalized, for a particle in an electromagnetic field, to $χ={\bf s}.{\bf p}/{\cal E}$, where ${\cal E}$ is the modified kinetic energy. Both $χ^o$ and $χ$ coincide and are conserved for minimal coupling (gyromagnetic ratio $g=0$) but are different and neither of them is conserved when the coupling is non-minimal, $g\neq0$, generating non-zero effective mass. For a chiral particle with $g=2$ in a constant electric field both helicities converge asymptotically to the same value. Helicity is also conserved for minimal gravitational coupling.

hep-th↗