Dynamics of Carroll Particles

Abstract

We investigate particles whose dynamics is invariant under the Carroll group. Although a single free such Carroll particle has no non-trivial dynamics (`the Carroll particle does not move') we show that there exists non-trivial dynamics for a set of interacting Carroll particles. Furthermore, we gauge the Carroll algebra and couple the Carroll particle to these gauge fields. It turns out that for such a coupled system even a single Carroll particle can have non-trivial dynamics.

22 pages, reference added

References in corpus (13)

• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Non-Relativistic Closed String Theory
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• Newtonian Gravity and the Bargmann Algebra
• Non-Relativistic Superstrings: A New Soluble Sector of AdS_5xS^5
• Newton-Cartan Supergravity
• On the Ultrarelativistic Limit of General Relativity
• Non-linear Realizations, Goldstone bosons of broken Lorentz rotations and effective actions for p-branes
• Group theoretical construction of planar Noncommutative Phase Spaces
• "Nonrelativistic" kinematics: Particles or waves?
• Dynamical sectors of a relativistic two particle model

Cited by in corpus (84)

• Gauging the Carroll Algebra and Ultra-Relativistic Gravity
• Carroll contractions of Lorentz-invariant theories
• Bridging Carrollian and Celestial Holography
• Carroll versus Galilei Gravity
• Fractons, dipole symmetries and curved spacetime
• Warped Conformal Field Theory as Lower Spin Gravity
• Carroll Expansion of General Relativity
• Holographic Reconstruction of 3D Flat Space-Time
• Connections and dynamical trajectories in generalised Newton-Cartan gravity II. An ambient perspective
• Conformal Carroll Scalars with Boosts
• On Higher-dimensional Carrollian and Galilean Conformal Field Theories
• Dynamics of Carroll Strings
• Carroll/fracton particles and their correspondence
• Remark About Non-Relativistic String in Newton-Cartan Background and Null Reduction
• Carrollian hydrodynamics from symmetries
• Carrollian manifolds and null infinity: A view from Cartan geometry
• Interacting Conformal Carrollian Theories: Cues from Electrodynamics
• Non-linear black hole dynamics and Carrollian fluids
• Planar Carrollean dynamics, and the Carroll quantum equation
• Gauges in Three-Dimensional Gravity and Holographic Fluids
• On free Lie algebras and particles in electro-magnetic fields
• Confined dynamical systems with Carroll or Galilei symmetries
• Dynamical structure of Carrollian Electrodynamics
• String Theory and non-Riemannian Geometry
• The Symmetries of the Carroll Superparticle
• Non-Lorentzian theories with and without constraints
• First order non-Lorentzian fluids, entropy production and linear instabilities
• One-Loop Quantum Effects in Carroll Scalars
• Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity
• Carroll limit of four-dimensional gravity theories in the first order formalism
• Scaling and conformal symmetries for plane gravitational waves
• The $\kappa$-Newtonian and $\kappa$-Carrollian algebras and their noncommutative spacetimes
• VSUSY models with Carroll or Galilei invariance
• Carroll versus Galilei from a Brane Perspective
• Tractor geometry of asymptotically flat spacetimes
• Geodesic motion in Bogoslovsky-Finsler Spacetimes
• Quantizing Carrollian field theories
• Carrollian Motion in Magnetized Black Hole Horizons
• Lorentzian Snyder spacetimes and their Galilei and Carroll limits from projective geometry
• Sturm-Liouville and Carroll: at the heart of the Memory Effect
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Deformed Carroll particle from 2+1 gravity
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• Fractons, non-Riemannian Geometry, and Double Field Theory
• Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part I: Generalities and Vectorial Descriptions
• Quantization of Carrollian conformal scalar theories
• Migrating Carrollian particles on magnetized black hole horizons
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• Carrollian limit of quadratic gravity
• Carroll membranes
• Multisymplectic Constraint Analysis of Scalar Field Theories, Chern-Simons Gravity, and Bosonic String Theory
• Torsion and anomalies in the warped limit of Lifschitz theories
• Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
• Hamiltonian Analysis of Non-Relativistic Non-BPS Dp-brane
• Bulk Reconstruction of Scalar Excitations in Flat${}_3$/CCFT${}_2$ and the Flat Limit from (A)dS${}_3$/CFT${}_2$
• Effective Chern-Simons actions of particles coupled to 3D gravity
• Enstrophy without boost symmetry
• Carroll Limit of Non-BPS Dp-Brane
• MultiCarroll dynamics
• AdS-Carroll Branes
• Quantum symmetries in 2+1 dimensions: Carroll, (a)dS-Carroll, Galilei and (a)dS-Galilei
• Lie Symmetries of Non-Relativistic and Relativistic Motions
• Looking for Carroll particles in two time spacetime
• Carroll-Schrödinger Equation
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Note About Integrability of Non-Relativistic String
• Carroll black holes in (A)dS and their higher-derivative modifications
• Asymptotic symmetries in Carrollian theories of gravity
• Planons and their Carroll-Galilei symmetries
• One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in $L^{\infty }$
• Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars
• Post-Carrollian Mechanics, Ideal Gas, and Gravity
• Fefferman-Graham and Bondi Gauges in the Fluid/Gravity Correspondence
• AdS${}_3$ Carroll gravity: asymptotic symmetries and C-thermal configurations
• Unique Carrollian manifolds emerging from Einstein spacetimes
• Sourced Carrollian Fluids Dual to Black Hole Horizons
• The Newtonian limit of orthonormal frames in metric theories of gravity
• Conformal Blocks in 2d Carrollian/Galilean CFTs and Excited State Entanglement Entropy
• Asymptotic symmetries in Carrollian theories of gravity with a negative cosmological constant
• Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
• Three-dimensional gravity and deformations of relativistic symmetries
• Circularly polarized periodic gravitational wave and the Pais-Uhlenbeck oscillator
• One-dimensional Carrollian fluids II: $C^1$ blow-up criteria
• A non-lorentzian primer