Modification of Heisenberg uncertainty relations in non-commutative Snyder space-time geometry

Abstract

We show that the Euclidean Snyder non-commutative space implies infinitely many different physical predictions. The distinct frameworks are specified by generalized uncertainty relations underlying deformed Heisenberg algebras. Considering the one-dimensional case in the minisuperspace arena, the bouncing Universe dynamics of loop quantum cosmology can be recovered.

5 pages; title changed, to appear in PRD

References in corpus (11)

• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• New realizations of Lie algebra kappa-deformed Euclidean space
• Loop cosmological dynamics and dualities with Randall-Sundrum braneworlds
• Twisted Statistics in kappa-Minkowski Spacetime
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Covariant realizations of kappa-deformed space
• The Big-Bang Singularity in the framework of a Generalized Uncertainty Principle
• Quantum Dynamics of the Taub Universe in a Generalized Uncertainty Principle framework
• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
• Yang's Model as Triply Special Relativity and the Snyder's Model--de Sitter Special Relativity Duality
• Polymer Quantum Dynamics of the Taub Universe

Cited by in corpus (54)

• Generalized Uncertainty Principle: Approaches and Applications
• Review on Generalized Uncertainty Principle
• Composite system in deformed space with minimal length
• Classical and quantum mechanics of the nonrelativistic Snyder model
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Deformed Heisenberg algebra with minimal length and equivalence principle
• 30 years in: Quo vadis generalized uncertainty principle?
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Generalized uncertainty principle or curved momentum space?
• Kappa-deformed Snyder spacetime
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Particle Dynamics on Snyder space
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Differential structure on kappa-Minkowski space, and kappa-Poincare algebra
• Snyder dynamics in a Schwarzschild spacetime
• Classical dynamics on curved Snyder space
• Natural Cutoffs via Compact Symplectic Manifolds
• Quantum field theory in generalised Snyder spaces
• Worldline Formalism in Snyder Spaces
• Associative realizations of the extended Snyder model
• Effect of Snyder-de Sitter model on the Black hole thermodynamics in the context of rainbow gravity
• Heisenberg doubles for Snyder type models
• The quantum N-body problem with a minimal length
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Relative-locality effects in Snyder spacetime
• Fermi equation of state with finite temperature corrections in quantum space-times approach: Snyder model vs GUP case
• Noncommutative fluid dynamics in the Snyder space-time
• Noncommutative Yang model and its generalizations
• On the viability of Planck scale cosmology with quartessence
• Polymer quantization versus the Snyder noncommutative space
• Associative realizations of $\kappa$-deformed extended Snyder model
• Generalized Extended Uncertainty Principles, Liouville theorem and density of states: Snyder-de Sitter and Yang models
• Macroscopic body in Snyder space and minimal length estimation
• Relative-locality phenomenology on Snyder spacetime
• Graphene in curved Snyder space
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Late time cosmic acceleration from natural infrared cutoff?
• Snyder Space-Time: K-Loop and Lie Triple System
• Generalized relativistic kinematics in Poincaré-invariant models
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Lie algebraic deformations of Minkowski space with Poincare algebra
• Relation of deformed nonlinear algebras with linear ones
• Twist for Snyder space
• CP violation, massive neutrinos, and its chiral condensate: new results from Snyder noncommutative geometry
• Relativistic Approach to the Hydrogen Atom in a Minimal Length Scenario
• Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
• A Stochastic Origin of Spacetime Non-Commutativity
• Noncommutative Spherically Symmetric Spaces
• Plane waves in noncommutative fluids
• Symplectic realization of generalized Snyder-Poisson algebra
• Realizations of the Extended Snyder Model
• Energy renormalization and integrability within the massive neutrinos model
• $\hslash$-perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking