Algebraic approach to quantum gravity II: noncommutative spacetime

Abstract

We provide a self-contained introduction to the quantum group approach to noncommutative geometry as the next-to-classical effective geometry that might be expected from any successful quantum gravity theory. We focus particularly on a thorough account of the bicrossproduct model noncommutative spacetimes of the form [t,x_i]=i λx_i and the correct formulation of predictions for it including a variable speed of light. We also study global issues in the Poincaré group in the model with the 2D case as illustration. We show that any off-shell momentum can be boosted to infinite negative energy by a finite Lorentz transformaton.

26 pages, 2 .eps figures; book chapter to appear in D. Oriti, ed., Cambridge Univ. Press

References in corpus (5)

• Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
• Algebraic {$q$}-Integration and Fourier Theory on Quantum and Braided Spaces
• Noncommutative geometry of angular momentum space U(su(2))
• On the classification of quantum Poincaré groups
• Noncommutative Model with Spontaneous Time Generation and Planckian bound

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• Physical Constraints on Quantum Deformations of Spacetime Symmetries
• On limitations of the extent of inertial frames in non-commutative relativistic spacetimes
• Field Theory on Curved Noncommutative Spacetimes
• Quantum Gravity models - brief conceptual summary
• Algebraic approach to quantum gravity III: noncommmutative Riemannian geometry