Fate of $\kappa$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes

Abstract

Here, we present an algebraic and kinematical analysis of non-commutative $\kappa$-Minkowski spaces within Galilean (non-relativistic) and Carrollian (ultra-relativistic) regimes. Utilizing the theory of Wigner-Inönu contractions, we begin with a brief review of how one can apply these contractions to the well-known Poincaré algebra, yielding the corresponding Galilean (both massive and mass-less) and Carrollian algebras as $c\to \infty$ and $c\to 0$, respectively. Subsequently, we methodically apply these contractions to non-commutative $\kappa$-deformed spaces, revealing compelling insights into the interplay among the non-commutative parameters $a^{\mu }$ (with $|a^{\nu }|$ being of the order of Planck length scale) and the speed of light $c$ as it approaches both infinity and zero. Our exploration predicts a sort of "branching" of the non-commutative parameters $a^{\mu }$, leading to the emergence of a novel length scale and time scale in either limit. Furthermore, our investigation extends to the examination of curved momentum spaces and their geodesic distances in appropriate subspaces of the $\kappa$-deformed Newtonian and Carrollian space-times. We finally delve into the study of their deformed dispersion relations, arising from these deformed geodesic distances, providing a comprehensive understanding of the nature of these space-times.

arXiv comment26 pages

References in corpus (59)

• Universal Intrinsic Spin-Hall Effect
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Doubly Special Relativity
• The principle of relative locality
• The BMS/GCA correspondence
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Galilean Conformal Algebras and AdS/CFT
• The exotic Galilei group and the "Peierls substitution"
• Doubly-Special Relativity: First Results and Key Open Problems
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Torsional Newton-Cartan Geometry and Lifshitz Holography
• Introduction to Doubly Special Relativity
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Newtonian Gravity and the Bargmann Algebra
• Exotic galilean symmetry in the non-commutative plane, and the Hall effect
• Carrollian Physics at the Black Hole Horizon
• Galilean-Invariant (2+1)-Dimensional Models with a Chern-Simons-Like Term and D=2 N oncommutative Geometry
• Flat holography and Carrollian fluids
• Carroll Structures, Null Geometry and Conformal Isometries
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Action Principle for Newtonian Gravity
• Carroll versus Galilei Gravity
• Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry
• Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity
• Non-Relativistic Gravity and its Coupling to Matter
• The Memory Effect for Plane Gravitational Waves
• Carroll Expansion of General Relativity
• Covariant realizations of kappa-deformed space
• Phenomenology of Doubly Special Relativity
• Torsional Newton-Cartan gravity from the large $c$ expansion of General Relativity
• Noncommutative Differential Calculus on the Kappa-Minkowski Space
• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
• Carroll symmetry of plane gravitational waves
• Quantum evolution in spacetime foam
• Gravity between Newton and Einstein
• Magnetic Carrollian gravity from the Carroll algebra
• Post-Newtonian extension of the Newton-Cartan theory
• Twisted Galilean symmetry and the Pauli principle at low energies
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Relativistic deformed kinematics from momentum space geometry
• On the structure and applications of the Bondi-Metzner-Sachs group
• Scalar field propagation in the phi^4 kappa-Minkowski model
• Living in Curved Momentum Space
• The origin of holomorphic states in Landau levels from non-commutative geometry, and a new formula for their overlaps on the torus
• Non-Lorentzian theories with and without constraints
• Tachyons in the Galilean limit
• General properties of the expansion methods of Lie algebras
• The $\kappa$-Newtonian and $\kappa$-Carrollian algebras and their noncommutative spacetimes
• Thermodynamics of a non-commutative fermion gas
• Carrollian limit of quadratic gravity
• Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
• Symmetries of $\kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?
• Quantum symmetries in 2+1 dimensions: Carroll, (a)dS-Carroll, Galilei and (a)dS-Galilei

Cited by in corpus (1)

• Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs