Curved momentum space, locality, and generalized space-time

Abstract

We establish the correspondence between two apparently unrelated but in fact complementary approaches of a relativistic deformed kinematics: the geometric properties of momentum space and the loss of absolute locality in canonical spacetime, which can be restored with the introduction of a generalized spacetime. This correspondence is made explicit for the case of $\kappa$-Poincaré kinematics and compared with its properties in the Hopf algebra framework.

arXiv comment18 pages

References in corpus (12)

• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Quantum Spacetime Phenomenology
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• String Theory and the Path to Unification: A Review of Recent Developments
• A brief review of "little string theories"
• Non-commutative space-time of Doubly Special Relativity theories
• De Sitter space as an arena for Doubly Special Relativity
• String theory: a perspective over the last 25 years
• Relativistic kinematics beyond Special Relativity
• Causal Sets: Quantum gravity from a fundamentally discrete spacetime
• Geometric interpretation of Planck-scale-deformed co-products
• Beyond Special Relativity at second order

Cited by in corpus (15)

• Generalized uncertainty principle or curved momentum space?
• Deformed relativistic kinematics on curved spacetime -- a geometric approach
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• Reinterpreting deformed Heisenberg algebras
• Modification of the mean free path of very high energy photons due to a relativistic deformed kinematics
• Time delays, choice of energy-momentum variables and relative locality in doubly special relativity
• Relativistic deformed kinematics: from flat to curved spacetimes
• Particle-antiparticle asymmetry in a relativistic deformed kinematics
• Momentum gauge fields from curved momentum space through Kaluza-Klein reduction
• $\kappa$-General-Relativity I: a Non-Commutative GR Theory with the $\kappa$-Minkowski Spacetime as its Flat Limit
• Cosmic Neutrinos as a Window to Departures from Special Relativity
• Anti-de Sitter Momentum Space in 3D and 4D Quantum Gravity
• $\kappa$-General-Relativity II: An Astrophysical Observable from a 2-Body system
• Generalized relative locality and causal sets