Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics

Abstract

We describe the deformed Poincare-conformal symmetries implying the covariance of the noncommutative space obeying Snyder's algebra. Relativistic particle models invariant under these deformed symmetries are presented. A gauge (reparametrisation) independent derivation of Snyder's algebra from such models is given. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided. Finally, an alternative form of an action yielding Snyder's algebra is discussed where the mass of a relativistic particle gets identified with the inverse of the noncommutativity parameter.

19 pages; Latex; title changed, 3 new references added and minor changes; to appear in JHEP

References in corpus (6)

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Cited by in corpus (47)

• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator
• Classical and quantum mechanics of the nonrelativistic Snyder model
• Covariant realizations of kappa-deformed space
• Topics in Noncommutative Geometry Inspired Physics
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Modification of Heisenberg uncertainty relations in non-commutative Snyder space-time geometry
• A Lagrangian for DSR Particle and the Role of Noncommutativity
• Snyder space revisited
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Particle Dynamics on Snyder space
• Doubly special relativity and translation invariance
• Conformal Invariance in noncommutative geometry and mutually interacting Snyder Particles
• Snyder dynamics in a Schwarzschild spacetime
• Electrodynamics of a Generalized Charged Particle in Doubly Special Relativity Framework
• DSR Relativistic Particle in a Lagrangian formulation and Non-Commutative Spacetime: A Gauge Independent Analysis
• Bumblebee gravity and particle motion in Snyder noncommutative spacetime structures
• Worldline Formalism in Snyder Spaces
• The emergence of Special and Doubly Special Relativity
• Dynamics of a Dirac Fermion in the presence of spin noncommutativity
• The Kepler problem in the Snyder space
• Symmetries of Snyder--de Sitter space and relativistic particle dynamics
• Noncommutative spaces, the quantum of time and the Lorentz symmetry
• Lorentzian Snyder spacetimes and their Galilei and Carroll limits from projective geometry
• Noncommutative fluid dynamics in the Snyder space-time
• Noncommutative Yang model and its generalizations
• Lorentz-violating dilatations in the momentum space and some extensions on non-linear actions of Lorentz algebra-preserving systems
• Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces
• Macroscopic body in Snyder space and minimal length estimation
• Snyder Noncommutativity and Pseudo-Hermitian Hamiltonians from a Jordanian Twist
• Relative-locality phenomenology on Snyder spacetime
• 1-D Harmonic Oscillator in Snyder Space, the Classic and the Quantum
• Generalized particle dynamics: modifying the motion of particles and branes
• Symmetries of $\kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?
• Generalized relativistic kinematics in Poincaré-invariant models
• Relativistic Particles on Quantum Space-time
• Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral
• Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric
• The E(2) Particle
• Particle on a torus knot: a Hamiltonian analysis
• Plane waves in noncommutative fluids
• Supersymmetric Extension of the Snyder Algebra
• Symplectic realization of generalized Snyder-Poisson algebra
• Aspects of noncommutativity in field theory, strings and membranes
• $\hslash$-perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking
• Snyder and their representation with creation and annihilation operators
• Theories on noncommutative spaces and deformed symmetries