A short introduction to $\kappa$-deformation

Abstract

In this short review we describe some aspects of $\kappa$-deformation. After discussing the algebraic and geometric approaches to $\kappa$-Poincaré algebra we construct the free scalar field theory, both on non-commutative $\kappa$-Minkowski space and on curved momentum space. Finally, we make a few remarks concerning interacting scalar field.

27 pages, submitted to the review section of International Journal of Modern Physics A

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• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• The principle of relative locality
• Introduction to Doubly Special Relativity
• Deformed Boost Transformations That Saturate at the Planck Scale
• Quantum $\kappa$-Poincare in Any Dimensions
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Observer-independent quanta of mass and length
• Coproduct and star product in field theories on Lie-algebra non-commutative space-times
• De Sitter space as an arena for Doubly Special Relativity
• Kappa-Minkowski space-time and the star product realizations
• Doubly Special Relativity and de Sitter space
• 2+1 gravity and Doubly Special Relativity
• Dimension and Dimensional Reduction in Quantum Gravity
• Waves on Noncommutative Spacetime and Gamma-Ray Bursts
• Relative locality: A deepening of the relativity principle
• Noncommutative Differential Calculus on the Kappa-Minkowski Space
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• Hopf-algebra description of noncommutative-spacetime symmetries
• Relative-locality distant observers and the phenomenology of momentum-space geometry
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• Relative locality and the soccer ball problem
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Local Field Theory ON $\kappa$-Minkowski Space, Star Products and Noncommutative Translations
• Lorentz invariant field theory on kappa-Minkowski space
• Scalar field propagation in the phi^4 kappa-Minkowski model
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• Living in Curved Momentum Space
• Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
• Star product realizations of kappa-Minkowski space
• Effective particle kinematics from Quantum Gravity
• Noncommutative fields and the short-scale structure of spacetime
• Differential calculi on quantum Minkowski space
• Deformed discrete symmetries
• Star product and interacting fields on $\kappa$-Minkowski space
• $\kappa$-Minkowski star product in any dimension from symplectic realization

Cited by in corpus (9)

• Pauli-Jordan Function and Scalar Field Quantization in $\kappa$-Minkowski Noncommutative Spacetime
• $\kappa$-deformed complex fields and discrete symmetries
• A bound on Planck-scale deformations of CPT from muon lifetime
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• Accelerated horizons and Planck-scale kinematics
• $\kappa$-deformed BMS symmetry
• Reproducing the effects of quantum deformation in the undeformed Jaynes-Cummings model
• Path integral quantization of a spinning particle
• The energy-momentum conservation law in two-particle system for twist-deformed Galilei Hopf algebras